Diana Athill's life has been full of unexpected twists. There was the broken relationship that led to a brilliant career in publishing, working with some of the world's most esteemed writers, and being regularly described as "the finest editor in London". At the same time she was engaged in a maze of love affairs that saw her cast more than once as "the other woman". And now, at 91, when most people's lives have slowed down considerably, Athill is enjoying perhaps her most exciting and unexpected new chapter - winning huge critical and commercial success as a writer.

Her latest memoir, Somewhere Towards the End, is shortlisted in the biography category for the Costa book awards (formerly the Whitbread); the category winner will be announced tomorrow. She says that she is very pleased about the shortlisting, "but I'm not allowing myself to get excited". In her five decades as an editor, Athill recalls having to "sit with authors of mine who had been shortlisted for prizes at those wretched dinners, saying, 'Now, we mustn't hope, we might easily not win', and then seeing their poor faces when in fact they didn't, and they were bravely pinning on a smile." Much better, she suspects, to let your feelings show. Athill is a stickler for directness.

We meet in her steaming, sweltering top-floor flat, and as we speak the room shades from light to dark without me even noticing. Athill is terrifically entertaining. Somewhere Towards the End is her sixth memoir, and came about at the suggestion of Guardian columnist Ian Jack, who was then running the publishing house Granta. He said that he would like to read a book about being old, to which Athill replied: "Are you MAAAAAD? What a dreary subject!" Her speech is peppered with sudden, plummy explosions. "He didn't nag me about it, but he probably mentioned it about twice, so it sowed a little seed and I began to think, 'Well, I suppose there are some things I could say, if I kept it very short.'"

The book is a series of interlinked essays that touch on everything from atheism to gardening and caring, and "it has done better for me than any other book I've ever written" says Athill. She thinks that this is because for "a long time age and death were taboo subjects in this country. My father used to walk out of the room when people tried to talk about death. He just couldn't bear it. But now I think the fact that I'm in my 90s and still compos mentis, and able to write and have a nice time, is encouraging to people. They can look at me and say, 'There is somebody who is old - which I am dreading - but there, it's not so bad.'"

Athill was born in 1917, to an upper-middle-class family in Norfolk. Like other women of her class and era, she was expected to bounce happily from school to marriage to children, but there were shadows in the background from the start. In her childhood memoir, Yesterday Morning, she writes about her mother having an affair, followed by a nervous breakdown. "She was obviously quite sure that nobody had ever done anything so terrible," says Athill. "And she spent her whole life working it out for our sakes. She felt ashamed, terribly ashamed of having done this wicked thing. But I think that she was, in fact, far from unique. I've always felt so sorry for her."

She suspects that her father blamed himself too. "He felt that he had been too unattractive and boring. I came across letters when they were both dead, and he said, 'Oh darling, I'm so sorry that I was never able to make you feel like Peggy felt about her husband' - Peggy was my mother's oldest sister. And that was my poor Dad, apologising."

That wasn't to be her only experience of infidelity. In Somewhere Towards the End, Athill writes of her pivotal relationship with Tony Irvin (known as "Paul" in the book) whom she met when she was 15 and he was an Oxford undergraduate. She fell deeply in love. "I was certain," she writes, "that once I was married to the man I loved I would be faithful to him for the rest of my life." Athill went up to Oxford herself, Irvin joined the RAF, and they were engaged. When he was posted to Egypt, she looked forward to joining him, and while she was never really a maternal person, she felt sure that they would have children.

Then Irvin stopped replying to her letters. His silence lasted two years. Finally, he sent a note, asking to be released from the engagement so that he could marry someone else. Shortly afterwards, he was killed. Athill was devastated by the broken relationship - a gloom that lasted 20 years. "Really, one did think that one's life had come to an end," she says. "Of course, in those days, you thought that you were looking forward to marriage as one's career, and it had gone."

From then on, Athill developed a great aversion to being tied down. "I hate possessiveness," she says. "I think what one should aim at is loving people, but not possessing them, and it's not easy, I suppose. To some people it is absolutely impossible." After Irvin, her next relationship was with a married man, as was one of the most significant affairs of her life - with the Jamaican playwright, Barry Reckord, whom she met when she was 43. "Being the Other Woman suited me so very well," she writes, which sounds distinctly cold. But she says that she has always conducted her relationships carefully. "If you're going to hurt other people, that is pretty awful," she says. "I think that if you're going to have extra-marital affairs, you should jolly well take the trouble to keep them extremely secret. Or else be the sort of couple that has an open marriage."

She describes her relationship with Reckord as a loving friendship, and he eventually split up with his wife - "not because of me" - and came to live with her. Their cohabitation began after their sexual relationship had petered out: they shared a flat, with separate bedrooms, and separate lovers. Indeed, Athill liked one of Reckord's girlfriends, Sally Cary, so much, that she "suggested that she should move in with us. It seemed to me that I would enjoy having her with us, and so I did."

All the while, of course, Athill was pursuing her glittering career. On leaving Oxford, she worked briefly at the BBC, before helping her friend and one-time lover, Andre Deutsch, set up his publishing house. Although £15,000 was said to be the minimum necessary to start such a company, they had just £3,000, attracted some brilliant authors, found themselves constantly struggling for cash, but critically successful. Over the years they published Simone de Beauvoir, Philip Roth, Jack Kerouac, Norman Mailer, Margaret Atwood, Laurie Lee, Stevie Smith and Marilyn French. Athill turned the experiences into her memoir, Stet. She says that the author she liked most was Molly Keane, who was "an absolute darling. And I suppose of all the men, the nicest was - is - John Updike." One of the less attractive characters was VS Naipaul; when Athill needed cheering up, "I used to tell myself: 'At least I'm not married to Vidia.'"

One of the authors whose writing style she most admired was Jean Rhys. "Jean used to simply say that she was trying to get it like it had really been. To get it right," she says. This is the hallmark of her own work. She uses metaphor rarely and perfectly, suggesting, for instance, that scarlet lipstick can make older women look "like a vampire bat disturbed in mid-dinner". "Jean used to say, 'Cut, cut, cut, cut,' and she was right," Athill says. "Accurate writing means accurate thinking."

Athill often seems the consummate observer, holding experience at arm's length, and turning it to the light. Of her attitude to sex, for example, she has written: "Quite early in my career the image of a glass-bottomed boat came to me as an apt one for sex; a love-making relationship with a man offered chances to peer at what went on under his surface." This clear-eyed approach is very useful for a writer, but seems a barrier to deep emotional entanglements. She admits that that first disastrous relationship was damaging, and made her equate "love and pain. I expected love affairs to go wrong. So, as time went by, I avoided involvements of real feeling. I steered clear of it. I kept things very light."

Her references to her career are always on the light side too; she writes of her laziness, and says that while she appreciates the plaudits regarding her editing, "I also know how little I had to do to earn this reputation beyond routine work and being agreeable to interesting people." This seems unlikely; you only have to read the chapter in Stet that describes the working relationship she developed with Gitta Sereny for Into That Darkness - an epic examination of a Nazi war criminal - to know that Athill's career involved more than some basic toil and amiable chat. The reason for her self-effacement appears to stem from her childhood, when the key rule, she writes, was "above all not to be vain and boastful".

In Somewhere Towards the End, she muses on the subject of regret, and decides that there are two after all: "that nub of coldness at the centre [of my character], and laziness". She doesn't regret being childless, although she was very excited when expecting in her early 40s - the pregnancy ended in miscarriage. Before that there were two abortions, at a time when the procedure was illegal. "Everybody knew someone who knew someone who knew someone," she says. "These addresses were handed on from friend to friend, and, in fact, for years, this address was scribbled on a piece of paper at the back of my dressing-room table, just in case any of my friends needed it."

I wonder whether there is anything about ageing that she left out of this latest book, so as not to scare people? "Just the boring things," she says. "I'm lucky, because, for instance, I've been spared incontinence - but I could easily not have been, and there's no fun in that. And one's digestion isn't so good. So there's the physical decay. You can't make that nice."

She gave up sex some years ago, and says she doesn't miss it. "It's like not being able to drink wine - at first I thought that was a terrible detriment, but once you can't drink something, and it makes you ill if you do, you don't mind giving it up . . . One reads from time to time absolutely obscene articles about senile sex - about how if you really go on trying hard enough, using all kinds of ointments, it can work, but for God's sake! It's supposed to be fun! If you need a cupboard full of Vaseline, you might just as well stop."

One of the great benefits of age, she says, is not caring what people think, although she suspects she never really did. She is looking forward to the category winners of the Costa award being announced tomorrow, and has been thinking of betting on the book she suspects will top the biography category - a life of Chagall - "just to cheer me up. If I don't win, I won't really mind not having the acclaim, it's not getting the money that I will mind. Because I'm always terribly broke, and how wonderful it would be to get that lovely cheque".

• Diana Athill's Somewhere Towards the End is published by Granta.