The offices of the London Review of Books are situated on the top two floors of a Georgian townhouse in the shadow of the British Museum. To reach them, you either brave the claustrophobically small lift or walk up five flights of brown-carpeted stairs, before emerging in a light-filled room containing a scattering of terrifically bright people sitting at computers, surrounded by piles of books and an air of quiet industry.

The windows on one side of the large open-plan room overlook the nurses' accommodation for the nearby University College Hospital, where someone has left a carton of orange juice to chill on a window ledge. The LRB's editor, Mary-Kay Wilmers, likes this view. She enjoys "seeing what the nurses get up to". On the other side, the windows overlook a fine Hawksmoor church spire, with carved heraldic symbols of a lion and a unicorn at its base. Wilmers doesn't have as much time for this. Most people would proffer some admiring blandishment about architectural style – but not Wilmers. "They're too fat," she sniffs at the stonework animals. And looking at them, it's hard not to concede that they are, indeed, a bit flabby.

The opposing London vistas, and Wilmers' reaction to them, seem to sum up her approach to editing what is now deemed to be the most successful literary publication in Europe. At 75, Wilmers retains both an insatiable curiosity about people (the nurses) and a healthy disregard for received opinion (the church). Both qualities course through the pages of the London Review of Books which, under her 22-year editorship, has become a highly regarded publication with an influence that extends far beyond the rarefied world of small-circulation literary magazines.

Founded in 1979, after the Times Literary Supplement was closed by a year-long industrial dispute, the LRB has a circulation of 64,038 (by comparison, according to 2013 Audit Bureau of Circulations figures, the Spectator has a circulation of 62,581 and the New Statesman of 28,495). The website attracts 575,000 visitors a month and there are a further 2,000 Kindle subscribers. At a time when most print publications are losing readers, the LRB's circulation is going up.

Partly, this is to do with the commissions. Alongside the usual run of densely typed book reviews, arts criticism, authors' diaries and classified advertisements offering writers' retreats in the Peloponnese, Wilmers has made a feature of the long-form essay. The essay, usually penned by a leading author and often running to well over 10,000 words, with barely a concession to the fanciful modern desire for accompanying photographs or illustration, has become the LRB's forte. These are the pieces that consistently challenge orthodoxy and take delight in a well-constructed argument; that dare to say things the rest of us might be thinking or that simply reveal something interesting or curious.

One of her recent favourites, says Wilmers, was a piece on "the language of bribery". At its best, the LRB long-form essay is clever, mischievous, fascinating and fluent. At its worst, it might go on a bit.

"I think there's an awful lot of short opinion around," says Wilmers, "and it's quite nice to find an argument in a piece that isn't just stated."

She is sitting in a small corner room on a sofa upholstered in countrified pale-green and red stripes. For unexplained reasons, there is an abandoned iron and an Anglepoise lamp on the floor that Wilmers had to step over, somewhat shakily in ballet pumps, to get to her seat. She is a small woman with a striking face and shrewd eyes. Her physical appearance is elegant but economical, crafted with the same precision as a judiciously edited sentence.

Does she think, in a modern, media-driven world where opinions are increasingly reduced to soundbites of 140 characters or fewer, that there is a thirst for longer-form writing?

"I think that must, to some extent, be the case because otherwise, why would we be doing so much better than other papers?" And it is true that, over the past year, the London Review of Books has found itself in the unusual position of being the centre of rather a lot of attention. There was a recent public spat concerning the lack of female reviewers in its pages, but much of the interest has been generated by the introduction of a Winter Lecture series – speeches delivered by writers in person on a particular topic and then printed at full-length as an essay in the magazine.

Hilary Mantel did one in February 2013, in which she called the Duchess of Cambridge "a shop-window mannequin". The Daily Mail promptly featured the "attack" on its front page and David Cameron was moved to comment that Mantel was "completely misguided and completely wrong".

When James Meek analysed the housing market in the pages of the LRB in January ("A housing shortage that has been building up for the past 30 years is reaching the point of crisis"), it triggered a national debate. The current issue carries an extraordinary 26,000-word piece by Andrew O'Hagan on his failed attempt to ghost the WikiLeaks founder Julian Assange's memoir, which was trending on Twitter before copies even hit the news-stands. The next issue features classicist Mary Beard's lecture on "the public voice of women", which has already caused a splash following her assertion that women who speak up in the public sphere are "treated as freakish androgynes".

Does she enjoy the controversies generated by the magazine? Her lips twitch into an almost-smile. Her eyes, below the silver fringe of her bobbed hair, crinkle at the corners. "I don't un-enjoy it," she replies carefully. She says she "never, ever would have predicted" the fall-out generated by the Hilary Mantel piece. "If you read the whole thing, it's really not… there's not much of an issue there. She was feeling sorry for her [the Duchess of Cambridge] more than anything."

What about the piece written in 2007 by Booker-prize winner Anne Enright concerning the parents of Madeleine McCann ("I was angry at their failure to accept that their daughter was probably dead. I wanted them to grieve") or Mary Beard writing in the immediate aftermath of 9/11 that America "had it coming"?

"'People will say America had it coming' is what she said!" Wilmers corrects impatiently. "Well, everybody said we would have bombs put through our letterbox." And did they? "No. It just caught on and it obviously touched a nerve because there were people who presumably did think that."

This is, in many respects, a key part of the LRB's ethos: it provides a space in which intelligent people can think differently; in which discomfiting thoughts can be voiced and provoking arguments can be aired with enough room to breathe.

The writer Marina Warner, who is one of the magazine's contributing editors, compares the LRB's pages to "a lively discussion among engaged people… I like its range – and its boldness in allowing different views and strong opinions, and the length of the pieces allows for developing arguments and laying out evidence." Andrew O'Hagan agrees: "The paper is enquiring, funny, political, ambivalent, and filled with a sense of risk."

Wilmers sees the LRB as an antidote to the sameness of opinion in the rest of the media. "Newspapers say the same thing over and over again and we're all horrified and collectively up in arms and there's normally more than one side to something," she says. "So if you hear somebody saying something coherent and intelligent that's not totally out of order, it's interesting to read it."

Twitter, with its emphasis on instant reaction and opinion-forming cliques is, she thinks, part of the problem. "Why do people feel compelled to agree with everybody? It would be quite nice if there was slightly less outrage about the same things all the time."

Is Wilmers on Twitter? "No," she says and then immediately contradicts herself: "I mean, yes, I am. I've only ever been on once, when Jenny Diski asked me to do something."

Her Twitter avatar, rather confusingly, is the image of a fresh-faced young woman. "That's my god-daughter, Flora Neve," she says sternly. No further explanation is forthcoming and I suddenly feel rather foolish for asking.

For all its success, the London Review of Books struggles to make money. It owes its continued existence to the generosity of Wilmers herself, who regularly siphons in cash from a family trust fund. Her German father was the founder of a multinational utilities company and her ancestors on her mother's side were Russian Jews who included the psychoanalyst Max Eitingon and Leonid Eitingon, a Stalinist agent responsible for masterminding the assassination of Leon Trotsky. Wilmers was born in Chicago, raised in New York, then moved with her family to Brussels aged nine and was sent to boarding school in England.

Did she like boarding school?

[Deadpan] "It was better than Brussels."

Having grown up abroad, does she feel like an outsider?

"You mean, do I feel foreign?" A pause. "When it suits me."

The family money means the LRB never has to worry about paying back its loans – in January 2010, the magazine was estimated to be £27m in debt to the trust. And yet it still manages to pay its writers at a base-rate of 30p a word (rising by a considerable margin if the article is longer than average). The fee for O'Hagan's piece on Assange was rumoured to be in five figures. Marina Warner says that payment is always processed quickly "and generously, by comparison with other papers".

Is it sustainable, I ask the LRB's publisher, Nicholas Spice? He looks vaguely shocked at the suggestion. "Oh no, it's not sustainable in financial terms," he says.

Spice has a pleasantly straightforward manner and a faintly military demeanour. He is the kind of man you suspect would be incapable of telling a lie, even though sometimes he probably should. "It loses a lot of money," he continues cheerfully. "The most important thing is that it has always had very generous support from its shareholders. And we've had the same shareholders since 1980, which is very unusual – I should think unprecedented – for a literary publication or arts organisation. The great thing is that we have been able to invest in creating a market for a very good editorial product."

The LRB has made inroads in other areas – there is a nearby London Review of Books bookshop, and a popular cake-shop that serves rosebud tea and gluten-free pistachio cakes – but even these, according to Spice, are only "near to breaking even".

"The great thing about the bookshop is it gives the magazine a location," Spice says, still looking on the brightest possible side, "and it's very good for our relations with publishers."

The seeming lack of financial constraint means that the LRB can be run in a charmingly old-fashioned, semi-shambolic manner. There is, admits Wilmers, "an element of whim" to each issue. Writers are not given much of a deadline – "we're not too fussy about time, then after a few months the piece comes in" – and the editors take a great deal of care over the copy. Every fact is checked and proofs are sent back to the writer with suggestions and queries and then, says Wilmers: "there's all that awful stuff about spacing and line-breaks, which I'm sure nobody notices, but we do".

Many of the writers have never met the staff and Wilmers herself has acquired a healthy degree of mystique.

"I've never met Mary-Kay Wilmers," says Adam Mars-Jones, a regular contributor, "and by the end of last year had come to think that was a good thing. If she liked my writing it seemed a bit rash to think she might like me as well."

The magazine goes to press on Friday night and the staff are often there into the early hours. Until recently, they ordered in supper from a local Indian restaurant much favoured by Wilmers. But she went on holiday a few weeks ago and returned to find that her staff had staged a silent coup and were getting their food from Ottolenghi instead. She doesn't like it as much. "Perhaps," she says, fiddling with the hem of her silk blouse, "it's just because I think, 'How dare they!'"

She's joking. I think.

One of the criticisms levelled at the LRB is that it can occasionally seem cosseted from the real world, run by an exclusive coterie of literary-minded north Londoners who don't have to worry about anything so vulgar as the bottom line. Wilmers is an established part of the liberal-leaning Primrose Hill intelligentsia: she was married to the film director Stephen Frears (the couple divorced in the 70s and have two sons, Sam and Will) and used to live next door to the biographer Claire Tomalin and her husband, the writer Michael Frayn. The playwright Jonathan Miller was down the road. Her best friend from Oxford (where she read modern languages) is Alan Bennett.

When I put this to her, Wilmers blinks. "Does everybody live in north London?" she asks herself, before going through a mental checklist of contributors and staff. "John Lanchester doesn't," she announces triumphantly. Spice says that most of their readers come from N and NW postcodes. Anywhere else?

"Clapham," he replies briskly.

But the LRB's tendency to pluck writers from the same limited pool of contributors has a more serious knock-on effect: they have consistently struggled to publish as many women as men, for instance. In 2013, they used 43 female book reviewers compared to 195 male, according to figures compiled by the American literary organisation Vida. The Paris Review, by contrast, achieved a 50/50 parity of men and women, while the New York Times book review published 725 women and 894 men. It is not just the review pages: over its history, the LRB has published 82% of articles by men and just 18% by women.

The issue was recently aired in a discussion on Open Book on Radio 4. The LRB declined to participate and issued a rather imperious statement claiming that the inequality in their pages was regrettable but reflected a wider discrimination in an imperfect world. The statement included a quote from Wilmers, given in a 2001 interview on the same subject: "I think women find it difficult to do their jobs, look after their children, cook dinner and write pieces," Wilmers said at the time. "They just can't get it done. And men can… They're not so frightened of asserting themselves. And they're not so anxious to please."

Listeners were duly enraged by the intimation that female writers were too busy scrubbing dishes to use their critical faculties. When I ask Wilmers about the episode, she visibly braces. "Obviously, over the years I've been discriminated against plenty," she says. "It started when I finished university and was told to go and learn to write shorthand by the Oxford 'head of women's appointments'. So, obviously, I know what it's like. I know what the problem is. And all I can say is that we hope to do better, we hope to get more female reviewers, blah blah blah."

But how exactly do they hope to do better? "Well, we hope we will find more women writers. We will look for more women." She glances anxiously towards the closed door that leads into the office and starts mouthing to me that she's been told not to say anything by her colleagues and they don't want her stirring it all up again. And yet, being of a naturally honest disposition, Wilmers can't help herself.

Surely that comment about women being too busy doing the household chores to write was spectacularly misguided? "Yes," she concedes. "I think the situation has changed because, certainly, when I was married, I did the washing up, I did the cooking, I looked after the children… I think that's much less the case now. Men do much more so women have less to do. So I think there has been a change but I do think men are more inclined to say 'Oh fuck it. I'll do whatever I want to do now. My career matters. I'll go and write a novel', whereas women are a bit more ho-hummy about their careers.

"All that has really changed since I've been working. When I was at Oxford, there was one woman for every 10 men. Imagine that. I mean, that's quite a statistic. So yes, it's changed a lot and there are many more women writers now in the LRB than there were 40, 50 years ago."

The irony is that Wilmers did end up becoming a secretary. After peripatetic upbringing that took her from America to Portugal, Switzerland, Belgium and England, Wilmers read French and Russian at Oxford. She had ambitions to be a simultaneous interpreter but ended up as a secretary at the offices of Faber & Faber. At the time, T S Eliot was director. "I was quite disappointed with him," she says. "He'd thank people for their 'gracious' letter and I though 'Gosh, what a terrible word.'"

She left Faber and had spells at the Listener magazine and the Times Literary Supplement before co-founding the LRB in 1979, originally as an offshoot of the New York Review of Books.

And all the while, she was coping with single motherhood and the emotional grind of raising a sick child. Wilmers's youngest son, Sam, was born with Riley-Day syndrome, a rare condition that affects the development of the nervous system. Sam was subject to seizures, poor co-ordination, failing eyesight and breathing issues. Today, in his 40s, he is almost blind but "thriving", Wilmers says fondly, "because he's got such a good character".

Her work, she says, was an integral part of keeping her sane. "I think I found it easier with the job than I would have without. I would have been that much more anxious about my son had I been at home watching him all the time."

She sees her role as editor in the same terms as the simultaneous interpreter she once wanted to be; they are both, she says, "ventriloquial occupations. It's speaking through other people. It's not that I'm not as egomaniacal as everyone else. It's just that I say a bit less."

She has written an acclaimed volume of family history, The Eitingons, but says she lacks the "inventiveness" to write a novel. I mention to her that I recently read Love, Nina, a delightful collection of letters written by Wilmers's former nanny, Nina Stibbe, while she was living with the family in the 80s. In it, Stibbe writes about Wilmers's habit of "piping up with a defining two words" while "everyone else [is] yakking and being boring and pointless".

Does she recognise that in herself? "Yes!" she says. "It's not what I most like about myself but I have to say, yes I do. But… um… it's that I don't necessarily have all the interim sentences. Those words are the two words I have. It's a bit of a defect."

But her facility for distilling a sentence makes her, according to Andrew O'Hagan, one of the great editors. "She and Karl Miller have done more for the British essay than anyone in the past 150 years," he says. "Mary-Kay works harder than any editor I know. And if this were France, they'd be posting the Légion d'honneur through her door every morning."

I wonder whether, at the age of 75, having lived through an era of unequal pay and endemic discrimination, part of Wilmers's attitude to the lack of female reviewers in the LRB is explained by a belief that people should just get on and do things rather than waste time complaining about them? "Yes, absolutely." Her feminism is, she concedes, "old-fashioned… I tend to take exception to men in a big way, but that's a slightly outmoded form of feminism."

Men as a general concept or men as individuals? "Men as a general concept, and individual men when they're behaving like men."

Is that why her marriage failed? "No. I mean, it was probably a foolish idea in the first place. I don't feel antipathy [towards men], I just am inclined to think that…" She breaks off. "It happened earlier this morning. You're talking to a male colleague, trying to get your point of view across, and then another male colleague walks across and agrees sagaciously with what the other man is saying. That always happens."

Does she say anything?

"Yes!"

I can't imagine, given her innate need to get on and do things, that she has altogether embraced the ageing process. "I feel appalled," she admits. "I keep thinking I'll wake up and find I'm not 75 any more." She has noticed a certain stickiness in the whirring of the mental cogs – when trying to convert dollars into sterling, for instance, or when she makes mistakes on the computer "and there's quite a lot of groaning" from her colleagues.

How will she give up this job, I wonder, when the time comes? "With difficulty," she says. "But the editor of the New York Review of Books is 10 years older than me. That's what I cling to."

The London Review of Books might not feature enough women in its pages. But there's no doubt that the one at its helm is pretty formidable.