I haven't heard anyone abbreviate "pious" to "pi" since my great aunt died – and she was born in the first world war. Joanna Trollope was born during the second world war, making her only just a generation younger, close enough to share a fondness for Enid Blytonesque slang – but that is where the similarities end. The novelist has the figure of a 14-year-old, the presence of a Hollywood star, and so much feminist fury about tabloid misogyny that whenever she sees women reading the Daily Mail on the tube, "I want to whip it out of girls' hands and just say: 'Please read something proper!'" She is without question the most contemporary 70-year-old I have ever met.

It's only afterwards that I realise she didn't mention her age once. The whole subject of ageing never even came up – which is odd, given what we talked about. It emerged this week that Trollope has donated her entire archive of manuscripts and notes to the Bodleian library in Oxford, so a preoccupation with mortality and posterity would have been perfectly natural. But Trollope seems to be too distracted by her own astonishment to have even thought about it. "Do you know," she marvels in her famous cut-glass vowels, "I'm just absolutely amazed that the donation's aroused any interest at all."

For years, all of Trollope's paperwork had been stacked up in a storage unit, until her PA's daughter offered to sort it out for her – "A perfectly lovely idea." There were handwritten manuscripts of her novels, along with cuttings of newspaper reviews, all her research notes, and every speech she has ever given. "I think it's a bit like making marmalade and looking at 50 jars lined up on the shelf in the pantry, and thinking, that is very satisfactory. I just thought, I can't bear to chuck this – this is the concrete evidence of what has ended up on the bookshelf."

Trollope laughs when I ask why her manuscripts are handwritten. "Decca, dear, I started before you were born. Nothing else had been invented." There were typewriters, of course. "But I'm not a natural typist. I'm of a generation who thought that if they learned to type, people would ask us to type, and we'd end up being somebody's secretary. A career for my generation of women was teaching, nursing, the civil service – or being somebody's secretary. And I was absolutely determined not to be somebody's secretary, so I didn't learn to type." She did enrol in a touch-typing evening class in her mid-40s, thinking she'd be "frightfully good at it", but was so daunted by all the "ace" 17-year-olds that she gave up and stuck to her pen.

Once the archive had been sorted into 50 orderly boxes, "all very museum-y and professional", the PA said it ought to be deposited somewhere. But Trollope was "frightfully squeamish about the whole thing. I said nobody will be interested, nobody will want it." Its market value has since been estimated at £100,000, but "honestly, I know I sound rather pi, but it never crossed my mind to sell it". She was amazed when the British library expressed an interest – and was staggered when the Bodleian "pounced".

She hadn't planned on making the donation public, until an old friend and Fleet Street editor got wind of it, but she hopes the archive will show aspiring novelists that "it's a messy business that requires an apprenticeship, and you have to learn how to do it by doing it. It's not this X Factor thing of thinking that if you want something enough, you should be allowed it. There's just something about learning the craft slowly, painfully, with failures and rejections, and with criticisms and unpleasantness." What was that process like for her? "Oh, it was horrible!"

Trollope was married to her first husband, a merchant banker, and working as a teacher while raising their two young daughters, when she began writing. The lukewarm reception for her early historical novels wasn't wildly encouraging. But then she fell in love with a playwright, who became her second husband, and he encouraged her to try contemporary fiction. Since then she has sold more than 5m books, seen her most famous titles – The Choir, A Village Affair, The Rector's Wife – become hit TV dramas, and earned millions of pounds. Her latest novel, Balancing Act, is about a woman facing a clash between her family and her business.

But no amount of success has ever managed to upgrade the literary reputation she was saddled with from the start, as a middle-brow chronicler of cosy, middle-class melodrama –"always associated with tinkling tea cups" – who churns out Aga sagas. "That was the sort of image I was given immediately – I suppose because of the way I sound, I don't know. But it was so dull. Because, actually, the books are quite subversive. I suggest wicked things like, you might have a better family life with friends rather than family – which is not very cosy. But I've always been given this sort of image." I ask if the cliches offend her, and she sighs heavily. "I think I'd save offence for something more serious. I think I just think, how tedious. How unimaginative. Mostly I think, how lazy. But you just have to exercise iron self-control."

Why has she never let rip at her critics? She sighs again. "Because I think that if you lose your temper with anybody, you know there's that heavenly moment of letting go of self-control, there's just that delicious moment when you let go and it's really, really exciting. And then it's ghastly. And I do know, if you lose your temper with anybody, you put yourself in their power, you make yourself vulnerable because you've lost control. So I wanted to convey a kind of bored contempt, I suppose."

Some of the literary establishment's sniffiness must have got to her, though, because she admits, "I thought the Bod would be too intellectual to want my archive. It never crossed my mind that such an august institution would be interested, it really didn't. I'm not a literary novelist. I'm not an Ian McEwan or a Martin Amis." The Bodleian's gratitude probably therefore means more to her than it could to McEwan or Amis, but she struggles to put the feeling into words. "It's the most fantastic sort of – I don't even want to say accolade. I just think, um, what do I think? I don't think, 'At last.'" Is it the sense of recognition? "Yes, something like that. It's just something quiet and very pleased. But it's quiet. I don't feel triumphant at all, I just think, how lovely, yes."

People always assume that Trollope is a true-blue Tory from the shires who lives in green wellies, but that reputation's wide of the mark too. After her second marriage ended 13 years ago she quit the Cotswolds for London, and now feels "completely urban". She has never belonged to a political party, has voted for all of them over the years, and describes herself as "the ultimate cross-bencher". Right now, she is absolutely hopping mad about the Conservative justice minister's recent decision to ban books being posted to prisoners.

"It seems to me too crackers to really be true. It seems to me utterly, utterly bonkers. If they're worried about books smuggling in drugs, why aren't the packages examined to make sure they're books?" Because Chris Grayling says the prison service don't have the time or resources. "Well, then there's some cheap person they could hire, surely. What this is doing is absolutely laying up unbelievably expensive trouble for the future. You know, leave aside all the inhumanity of it, it's such a ludicrously impractical, extravagant way of thinking. Because it's not rehabilitating these people who need it so badly, and therefore they're going to come out and wreck the lives of their women and children and men friends and everything and they're going to offend again and cost the taxpayer yet more and be kept expensively in prison for another term. It's just the most bogglingly bonkers thing I've ever heard. I cannot believe it, and if they say they can't afford it then there should be somebody who just undoes parcels. What about getting someone off the dole and training them and paying them the minimum wage? What about getting a school leaver or an apprentice?"

Trollope spends quite a lot of time in prison. She gave a talk in a young offenders' institute recently. "I talked to them about their lives, and about narrative. I said men aren't very good at self-reinvention, women seem to be much better at it. But you needn't identify yourself by your lowest moment. You don't have to be the people you were when the judge said, 'you're going down'. There is another chance. And I talked to them about education and reading, and the value of narrative and what you can learn about human nature from narrative."

I try to picture Trollope saying this to a group of young offenders, and wonder if she spoke exactly as she is now. "Yes. And I sounded exactly like this." Other writers don't seem very keen, she reflects, on giving talks in prisons, so I ask if they think prisons are scary. "But they're so not scary! They're riveting places."

For years Trollope has been a patron of a specialist school for children "deemed ineducable and uncontrollable". The annual cost per child is more than £150,000 – but within three to five years, she says, 60% are able to re-enter mainstream education. "It's perfectly astonishing." She talked about the school during her recent prison visit, and one of the prisoners told her that if he'd been sent somewhere like that, "not only would his life have been different, but so would all the people's whose lives he wrecked". But Grayling thinks the prison system provides too many luxuries, and that prisoners will benefit from a crackdown. "Reading is not a luxury!" she explodes. "It's a necessity. It illuminates people's lives."

Were Trollope a young woman today, however, she's not sure that she would become a writer. "That's a very good question. I think it's 10 times harder now, because you see, when I started it wasn't a sexy profession at all. It was a rather dusty thing you did by yourself, and nobody took it seriously. I remember people would ring up and say, 'I'm going to come round for coffee,' and I'd say, 'Well, no, actually I'm writing,' and they said, 'Oh that's fine, I'll only be 10 minutes,' you know. Now people are always saying to me, 'I'm writing my novel.' "But I think it's incredibly hard now. I really do. To make a career, earn a living from it – I don't think it would be possible now. And if you have a sudden explosion of success, I think for a lot of people the sudden media attention and spotlight – 'Write another one! Sing and dance for us! Show us what you can do! Take your clothes off! Are you gay? Are you not gay?' – I think they find it too much. Luckily, I didn't have to deal with that."

The one problem Trollope has had to deal with since long before she even became a writer is other people's envy. "Yup, yes," she says quietly. The eldest of four, she was always a high-achieving child, and contemporaries recall her as an intimidatingly self-possessed undergraduate at Oxford. By now she's so used to others' envy that I wonder if she even notices it any more. "I always notice it," she says softly. An overweight female interviewer once told her: "'You know you've taken my chance to be thin. I'm like I am because you're like you are.' It was deranged. It was absolutely deranged. But now it makes me just feel ... I just feel sad and tired about it. For them. There's nothing I can do about it. Except, you know, be nice to them. But I don't feel resentful about it any more. I'm afraid it's just not my problem."