I have a low-level dread of artists' studios, which tend to be full to overflowing with the (to me) highly distressing detritus of creativity: encrusted paint; cruelly abandoned canvases; ghostly dustsheets. But I find that I can just about cope with Jenny Saville's work space, which is in a shabby office building in Oxford, owned by Pembroke College.  For one thing, its scale works against claustrophobia; though she has had to remove ceiling tiles in a few places, the better to accommodate the taller of her paintings, it is nevertheless as big as a small supermarket. For another, it is divided, albeit haphazardly, into zones – broken-backed art books here, shrunken tubes of paint there – with a few feet of clear floor between. As we settle down with our mugs of Earl Grey tea, the spring rain fizzing against the windows, the feeling is almost – if not quite – cosy.  Only then, out of the corner of my eye, I see it. A portrait: a woman, her neck at a difficult angle, her head tipped back, her unseeing eyes a pair of cloudy marbles (I know without being told that the model who sat for this work is blind). Now I'm not so cosy. The trick of the painting, the reason it is so hard to pull one's gaze from it, lies with the way it captures its subject's extrasensory watchfulness. She is sightless, and yet you feel, somehow, that she sees right into you. Art critics, anxious to emphasise the resonance or beauty of a particular work, have a tendency to exaggerate. They will tell you, for instance, that a canvas seems almost to vibrate, such is its power. But this painting moves well beyond vibration. No superlative I can think of seems to do it justice. It's uncanny. If I heard its subject softly breathing, I would hardly be surprised.  A painting similar to this one – I find out much later that the girl in question is called Rosetta; she lives in Naples, and was so determined not to be on the receiving end of pity she interviewed Saville at length before agreeing to sit for her – will star in the forthcoming retrospective of Saville's work at Modern Art Oxford, the artist's first solo show in a British public gallery. (It tells you a lot about contemporary art – its whims and its desires, its peculiar snobberies and its deranged hierarchy – that Damien Hirst, whose work appeared alongside Saville's at the Royal Academy's Sensation show in 1997, is having his first solo public gallery show at the rather more grand Tate Modern; but we will come back to him.) Will Rosetta, part of Saville's Stare series, have the same effect in its pristine galleries? Almost certainly, though she will also have competition. Saville's work – she remains best known for her voluminous and unsparing early nudes – is nothing if not startling.  "There's a painting called Fulcrum," she says. "I used to call it The Bitch when I was making it, because it was so difficult to move about. But when I saw it again [recently], even I was shocked by how big it is." She shakes her head, mournfully. "I'm sort of impressed that I once had that sort of energy. The drive I must have had. I can't believe I was only 21. That's so young, and yet I was so determinedly serious about making art." Her voice runs on. "It's cathartic, too, though, seeing these paintings again. When you're in your studio, you've got so much work around you, you don't always see an individual piece for what it is. You think: 'Oh, so that's what I was doing.' Not that I can say I'm hugely looking forward to it [the opening]. I mostly see failings in the work – which is normal, isn't it?"  Has her confidence grown in the years since Sensation? "No, not at all. The older you get, the more doubtful you become, though I mean that in a good way. It's like being an athlete. You get quite fit on your toes when you're really pushing. But then you finish a piece, and you have to start all over again. On the other hand, I don't have anything like the traumas I used to have, throwing paintbrushes or whatever. I used only to work on one piece at a time, and that's where the trauma came. Now I move between paintings. When I start getting a bit dogmatic, I switch."  I look around the studio. From where I'm sitting, I can see no fewer than six canvases carefully arranged against the wall (not Rosetta, though; I have my back to her, so I can concentrate). Are these all works in progress? "Most of them, yes." She eyes them, warily. "It is odd to be showing in Britain. I've been shown a lot in America; that's my favourite place to show. We're quite conceptually driven in Britain. There's less guilt about being a painter over there."  Does she feel guilty? Surely not. People have talked of her, reverentially, as the heir to Lucian Freud pretty much since she left art school. "No, I don't. Not at all. Painting is my natural language. I feel in my own universe when I'm painting. But, in Britain, there has been a drive in art schools to describe and to rationalise what it is that you're making, and that is a death knell to painting. Painting doesn't operate like that. It works on all the irrational things. If you stand in front of Willem de Kooning's Woman, I, you can't unravel with words how that works on you. In America, painting is embraced, perhaps because one of the last great moments of painting was in New York, with de Kooning and Pollock."  She hesitates. "I'm not anti conceptual art. I don't think painting must be revived, exactly. Art reflects life, and our lives are full of algorithms, so a lot of people are going to want to make art that's like an algorithm. But my language is painting, and painting is the opposite of that. There's something primal about it. It's innate, the need to make marks. That's why, when you're a child, you scribble."  Jenny Saville was born in Cambridge in 1970, one of four children. She knew early on that she wanted to be an artist. "I was conscious of it as an idea from about the age of seven," she says. Her parents were both in education and, when it came to creativity, were encouraging. "We had this big old house, and in a corridor downstairs, there was this weird cupboard. I kept nosying around it, and eventually my mother gave it to me: it became my first studio, and no one else was allowed in. I would wake up every morning, and I just couldn't wait to get in that room, because I always had something on the go."  Later, she was encouraged by her uncle, an art historian, to whom she remains close (he lives near her studio in Oxford; they like to eat lunch together, and talk about Prussian blue). "When I was about 11, he gave me a section of hedge, and told me to observe it for a whole year. So I did, and I learnt such a lot about how nature shifts, and the necessity to really look."  She sees my face. "It wasn't weird at the time! It's only weird when I tell other people. I'm so grateful to him. Later on, he took me to Venice, and it wasn't just that he said this is Titian, and this is Tintoretto, or whatever. At six o'clock one morning, we went to draw at the fish market at the Rialto bridge. Great art wasn't something far away; it was part of life. We would go and drink in the same bar Rembrandt drank in; it was as fundamental as that in terms of the working life of the artist. All this helped me so much. I never questioned my ambition. I never thought: I'm a girl, I can't do this. It was only when I got to art school that I realised that the great artists of the past were not women. I had a sort of epiphany in the library: where are all the women? Only then, as the truth dawned, did I start to feel pissed off."  She went to Glasgow School of Art, an institution that instilled in her an "amazing" work ethic, and which set great store by life drawings; students had to produce 36 such sketches a term, and dedicate the hours between 7pm and 9pm every day to working with a model, even if their interests lay with abstract art.  Saville believes this gave her a kind of freedom. "Picasso wouldn't be Picasso without his academic training. That's why he nails it. The wildest distortions stand up, even if they're crazy. The point is that destruction is fundamental to the process; without it, you never get anywhere interesting. But fundamental to that is knowing what you can excavate from the destruction."  At Glasgow, she won every award going, among them a six-month scholarship to Cincinnati University, where she was captivated – if this is the right word – by the sight of obese women at shopping malls. It was these women who inspired her 1992 graduate show and who, in their turn, caught the eye of the collector Charles Saatchi – though her interest in flesh was hardly a new thing. As a little girl, she found the sight of liver turning from puce to grey-green in the pan "thrilling". She remembers, too, sitting on the floor, aged about six, and looking up at her piano teacher's thighs under her tweed skirt; they rubbed together as she played. "I was fascinated by the way her two breasts would become one, the way her fat moved, the way it hung on the back of her arms."  After tracking down and buying up the work already sold at her degree show – this was how he came by two of her most famous paintings, Branded and Propped – Saatchi then commissioned her to spend two years working on pieces to be shown at his own gallery in Young British Artists III.  "I think everyone has their squabbles with Charles," she says, now. "That's the nature of the situation. But the marriage of a new generation of artists from all kinds of backgrounds with this man who wasn't from the establishment… You have to understand that he energised a whole generation, and he engaged Britain in contemporary art. He had the money, and he said: make whatever you want.  "I was only 22; it was a dream come true. I can't say anything bad about Charles because I'm so glad he was there. Suddenly I didn't have to wait until I was 45 to be at a certain gallery. I'm 42, and I'm still younger than de Kooning was when he had his first show. It's incredible how much has changed in 20 years, and quite a lot of that is down to Charles. When I graduated I would have been hard pressed to think of a single woman who showed in a museum, and now women are directors, curators…" Her voice trails off. She can't go on, I think, because the unavoidable truth is that there are still relatively few women artists who are deemed worthy of museum exhibitions.  Am I right? She doesn't answer, or not directly. "When my show opened at the Saatchi gallery, I met David Sylvester [the art critic, who died in 2001] at the door. In the end, we became great friends. But on that day, he said: 'I always thought women couldn't be painters.' Later, I asked him why, and he said: 'I don't know. That's just the way it has always been. That's how it is.' He was right, but I think it's beginning to shift, now. Apart from anything else, there's been a sea change in what we consider to be the canon. Tracey Emin's quilts are art, whereas in the Sixties, they would have been deemed to be craft."  To coincide with her retrospective, Saville will be putting two pieces in the Renaissance gallery at the Ashmolean Museum. "I was standing there the other day, and it's full of nude women all painted by men. I'm the first woman to show in the room, which is great, but it's also obscene." She pauses. "Actually, it's not even obscene. It's just… silly."  In 1994 Saville returned to the US to observe operations at the clinic of a New York plastic surgeon. She then painted women with the surgeon's black markings on the contours of their bodies, so that they resembled living, breathing dartboards. This led in turn to Closed Contact, a series of photographs by the fashion photographer, Glen Luchford, of Saville's naked body pressed against Perspex and shot from below (Saville fattened herself up for this, the better that her flesh appear squashed and distorted). The subtext of this work is, of course, familiar now. But it wasn't at the time.  "When I made Plan [showing the lines drawn on a woman's body to designate where liposuction would be performed], I was forever explaining what liposuction was. It seemed so violent then. These days, I doubt there's anyone in the western world who doesn't know what liposuction is. Surgery was a minority sport; now that notion of hybridity is everywhere. There's almost a new race: the plastic surgery race."  These experiences, however, have cast a long shadow. She is still interested in the idea that many people hold fast to a notion that their natural self isn't the "real" them, and her work continues to be preoccupied by what she calls a sense of in-betweenness. "That's why transsexuals and hermaphrodites have become interesting to me. I want to be a painter of modern life, and modern bodies, those that emulate contemporary life, they're what I find most interesting."  More recently, she has been inspired by motherhood (she has two small children). "People told me [before I had children] that I wouldn't be able to engage with my work in the same way once they were born." Which people? Were they women? "No!" She laughs. "They were guys. Anyway, they were wrong. I enjoy the work 10 times more now. It's still a necessity to me, something I have to do. But I'm more carefree. Partly, it's watching them – the total freedom they have, scribbling across paper, the way they paint without any need for form. I thought: I fancy a bit of that myself."  Since they were born, she has produced a series of drawings, Reproduction, which nod to nativity sketches by Leonardo da Vinci and Michelangelo but are informed by her own experiences – a friend photographed her as she gave birth – so that mother and child are viscerally connected rather than soppily idealised. (Just so there is no misunderstanding, Saville is naked in these drawings, and the baby in her arms is lain on a belly swollen with a child yet to be born.)  Before I leave, we walk the studio, looking at the work that is still in progress (Saville is remarkably cool about this; only one canvas is turned to the wall to protect it from my gaze). "In these pieces, I'm trying to get simultaneous realities to exist in the same image," she says. "The contradiction of a drawing on top of a drawing replicates the slippage we have between the real world and the screen world. But it's about the memory of pictures, too. I'm directly referencing other artists: Manet, Titian, Picasso, Giorgione." If she has any sense of the daring involved in this – the sheer chutzpah of it – she isn't letting on. How does she know when something is finished? "When it starts to breathe, then I'm on the home straight."  We talk, too, about other people's work. She loved both Gerhard Richter at Tate Modern and Lucian Freud at the National Portrait Gallery. "It's sad he [Freud] is not going to make any more paintings," she says. "But I'm trying to work out whether he can be seen as a great artist, or whether he is a great portrait painter. I mean, why shouldn't he be a great artist? But then you look at Richter, and you wonder. Richter is definitely a great artist in the fullest sense of the word."  What about Damien Hirst? Has she seen his show yet? "No, but I will." I don't ask her what she thinks about him, but she tells me all the same, in her straightforward way. "I can tell you exactly the moment my feelings about him changed," she says. "He was the most brilliant artist right up until the time [2006] when he did this homage to Bacon at the Gagosian [A Thousand Years & Triptychs]. He did these vitrines, which I felt were dreadful. His work has become much more about the mechanisms of the art world than the art itself, and that must be quite a lonely planet for Damien to exist on. It's as if he has beaten his own horse. It's like the soul has gone."  Will this ever happen to her? At the start of the 21st century, she was, after all, one of the most expensive contemporary artists in the world. But, no. Of course it won't. Her life is here, in the studio. Even as we talk, and she is good talker, I can feel a part of her itching to get back to work. "I like all the bits up to hanging a show, and then I disengage," she says. "I don't even know my own collectors. All the razzmatazz: the market, the auctions. I'm quite immune to it. I know it's part of the process. But when you get in the studio, none of that will help you to make a better painting."
Rachel Cooke: Jenny Saville's nudes are firmly in the vein of Lucian Freud, yet only now is she having her first major British solo show