POSING for a photograph in front of her painting Muse, Jenny Saville turns to look at it for a moment. In front of her is a kaleidoscopic monochrome image of entangled bodies and body parts. “My son says this one is ‘a puddle of boobs’,” she tells me.

To be fair, he’s not wrong. Friday morning at Modern One in Edinburgh and we are surrounded by naked flesh. It is the hanging stage of Saville’s retrospective show at the gallery. There are paintings already on the walls, others on the floor waiting to be put on the walls and one or two on the walls but covered with paper (“It has to decompress or whatever it does,” Saville explains).

And, yes, there are breasts. Nearly all of these paintings are of and about the body. Here are Saville’s early self-portraits, in which the scale – both the paintings themselves and the representations of the anything-but-size-zero human bodies they portray – is the first thing you notice. Here, too, is Fulcrum, a monumental nude portrait of Saville herself with her partner Paul McPhail’s mother and sister, all three of them piled up on top of each other, from 1999. Here are paintings where naked bodies sprawl and multiply and stack up on top of each other.

Here, in short, is the work of one of the UK’s most celebrated contemporary painters.

And here today is the painter herself, up from her studio in Oxford. Hair pulled back, petite and wrapped up in a black overcoat walking me around the space, she is thrilled at the very idea of a show at Modern One.

“I was in Perth last Christmas with my relatives. We had a couple of hours and I said, ‘Oh, let’s come to the museum’. And we walked through these rooms and I said to my kids, ‘If I ever show in Scotland I want to show here in these rooms’. And two weeks later Simon Groom [director of the Scottish National Gallery of Modern Art] called me and offered me the show.

“It’s got the most wonderful light. It’s a wonderful place to show. I’m really happy,” she says. You can tell.

The retrospective will form part of the latest tranche of the gallery’s ongoing Now exhibitions and Saville is walking me through the five rooms this morning. Five rooms and 25 years of her painting life, stretching back to her time at the Glasgow School of Art which, she says, is where she became an artist.

Saville is the best kind of advocate for her own work. She’s eloquent, takes her art seriously, but finds the humour in it too. In short, she can talk both Bronzino and boobs if so required.

Interviewing her in 1993, when she was the Charles Saatchi-approved next big thing, journalist Hunter Davies wrote that Saville spoke with “a distinct Scottish accent, rather Kelvinside-y”.

If that was ever the case it has long gone, although other markers of her time in Glasgow have hung on, it seems. “Jenny,” I ask at one point, “are you still a Rangers fan?”

“I am a Rangers fan. I’m a bit disappointed in the last few years, but my partner is still adamantly a Rangers fan.

“I’ve got a daughter who is more into tennis. She finished number three in the country last year at age 10. So I’ve become more into tennis because of her.

“But my partner Paul, he is obsessed with it and I have to listen to hours of moans and groans about what’s being going on at Ibrox.”

There are more concrete traces of her Glasgow years on display at Modern One. That includes her canvas Trace, a painting of a naked female back on which the marks of recently discarded underwear can still be seen imprinted.

Trace can be seen in the first room of the exhibition which contains her Glasgow paintings. Propped (“a Rubens nude politically corrected,” the critic Andrew Graham Dixon suggested in a rather disapproving review when it was hung in the Saatchi Gallery in 1994), is one of her most familiar self-portraits.

Here it is hung as it was at Saville’s degree show, opposite a mirror in which you can read the backwards writing scratched into the canvas – the nearest she ever got to conceptual art.

When you see these paintings again, I ask Saville, what’s your relationship with them a quarter of a century on?

“Sometimes I think, ‘Wow’. The big painting Fulcrum, that’s massive. That’s ambitious, man. I was so young, and I made such an ambitious painting.

“But mostly I see the graft that I did to get them into shape. And I can re-engage with the feelings that I had. ‘Oh, I couldn’t get the nose to work.’ Those moments. It recalls memories of that time. I can hear the music that was playing in my studio at the time I was making those paintings.”

Saville, who is now based in Oxford, was actually born in Cambridge, and spent her childhood moving around a lot before coming to the Glasgow School of Art in 1988.

It was the fact that it was a painting school that brought her here. “Every day you walk up those steps it makes you become an artist,” she says.

She was as devastated as everyone else when it went on fire. “I actually think the first service did an amazing job. They were lucky the whole thing didn’t burn down. When we were there we used to smoke fags. The lecture room was a sea of cigarette smoke. The floor was turps-soaked. So, when it started I thought that the whole building is going to go up. We were lucky we didn’t lose it all.”

Saville was out of the gate fast. Saatchi famously bought work from her degree show and then offered her a contract. He also promoted her as one of the Sensation generation (alongside Hirst and Emin and the Chapman brothers and everyone else who made Britart cool in the Cool Britannia era). By 1994 her work was even gracing the cover of the Manic Street Preachers’ most difficult album The Holy Bible.

But Saville never felt part of that YBA gang. Her art drew on other models, was interested in different conversations, was fed by different desires, different experiences.

What it did share, though, was the scale of ambition. We are standing in front of Fulcrum. The size of the painting is the first thing that hits you. How long did it take to paint?

“Fulcrum took 18 months. But it’s not 18 months on a single painting. Often, I’ve got one or two that are really difficult, trudgy paintings. And then around it I have ones that are very easy. You get a reward for grafting on one from the other one.”

She points across the room to Hyphen: two huge heads that seem almost grafted onto each other.

“Fulcrum was really difficult, and Hyphen became super-easy. That’s why I put them opposite. Everything about Hyphen was so pleasurable in the making. I’d learnt everything in that painting,” she says, pointing to Fulcrum. “And the reward was making Hyphen. They’re like a diptych in a way.”

The thing I want to ask about Fulcrum, I say, is what was the conversation … “While we were doing it?” she interrupts.

Not quite. I was thinking more of the conversation when you first suggested the idea to Paul’s sister and mother. It doesn’t look a comfortable pose, does it? And it’s pretty intimate, Jenny.

“To be honest, they’ve been amazing in my life. They’ve been up for everything.

“It was hilariously good fun to do. It was a bonding moment, put it that way.”

Paul’s mother is 85 now. “She’s lost loads of weight. Actually, this Christmas she was saying: ‘I’ve lost all this weight. My boobs are nearly hitting the floor. I’m a great model again.’

“Now I have lots of people wanting to model. Before it was much more difficult. It’s a tricky thing to be prepared to do.”

As we stand in front of this nude self-portrait it reminds me that coming here today I was trying to think of male artists who are bodies as well as eyes. Picasso in his bullish machismo certainly. Schiele in his vulnerable intimacy. But Vermeer?

When it comes down to it, the male gaze is about looking more than being looked at, isn’t it?

“Rembrandt’s got a body,” Saville suggests. Agreed. The thing I’m getting at, I suppose, is an idea that women artists are more incarnated; their art – from Frida Kahlo to Tracey Emin and Cindy Sherman is so often about the self. Or about the female body. About being looked at.

Saville takes onboard the idea but I’m not sure she totally accepts it.

“When I started working like this the kind of masculine aspect of my work – the macho scale and everything – was seen as a male trait, not a female trait.”

Then again, she points out parenthood has been one of her subjects.

“I would say dealing with motherhood was a big decision for me. I was always seen as this super-hard-working, serious painter. So it was a big decision to put the idea of being a mother into the work. I could just have been a mother on the side, almost. But it was so profound and so incredible, giving birth and watching these infants growing, and so human that I just couldn’t avoid it.

“I’m Picassoesque in that sense. Everything in my life ends up in the work. It’s like a dam that opens and I just can’t stop it. So I just had to put it out and I’m really happy that I was brave enough to do that.

“These things were shocking to me. It just changed everything. I’ve spent my life trying to paint flesh and I was growing it inside my body. And the experience of painting that every day while I had this growing body inside me, I’ve tried to trap that in the work.”

Her children – a boy and a girl – are 10 and 11 now. Even watching them draw – the spontaneity they bring to the task – has fed into her work. You can see it in the freedom of her mark-making in her later paintings, the looseness and openness of them.

That said, the subject remains the human form. “I’m a deeply figurative artist. I just think it’s one of the hardest things you can do. And to try to navigate it and make it relevant today has been my life’s work really.”

That level of ambition is thrilling. It speaks, too, to a self-belief that is ready to step up and accept that she is in dialogue with the great artists.

“I’m not a custodian of the past,” she qualifies. “I don’t want to be nostalgic. All of the past is in my work and I engage with that every day. But I want to make work that feels like it belongs today, in people’s bodies, in lived bodies today.

“I think some people think that if you’re a figurative artist then for some reason you’re not as clever. There’s a perception around figurative painting that means … not that you’re not a serious artist, but it’s difficult to not be a naff figurative artist. It’s very easy to be a cliche. So, to access Rembrandt, Picasso, Titian; that’s a life’s work. And I agreed with myself that that is enough. I’m going to try to be the best.”

We’ve come to the final room in the exhibition. On the wall in front of us is Olympia, a large canvas that is both figurative and abstract (Cy Twombly is as much an influence on Saville as anyone).

A black man and a white woman are displayed against a cityscape. And near the bottom of the canvas there’s a shadow that Saville says makes it look like one of a series of stacked images on your computer screen. Figuration meets abstraction.

At least I think it’s a man and a woman. I count the legs on display. Are there actually three bodies on show here, Jenny? “Multiples,” she replies. “There’s loads of legs. They sort of grow together.

“I worked with this wonderful couple. He’s the manager of Sainsbury’s in Oxford and the woman works with my aunt. I like this idea of black and white flesh together, the challenge of that and the way we live in a much more multicultural society.”

It’s another carnal painting, of course. You could read it as sexual. I wonder how Saville engages with that history of the male gaze in art?

“I think I’m asserting my right to look. When I started out in Glasgow I realised that to do that was sort of trespassing on somebody else’s tradition.”

She turns back to the painting. “I look at her body and his body. I’m not the one being looked at and I think as an artist I’ve tried to play with the idea of the gaze.

“My early work is probably a secret dialogue between women to say, ‘Oh, yes, I feel like that too.’ But as my work’s developed it’s become less about that – probably because I became better known.

“Now I’m in the game of art. I’ve justified my position.” And that’s how you see it? As a game?

“It’s all a game, isn’t it? And a dialogue with history. I’m definitely not so worried about being a contemporary artist.”

And yet of course she is. The bodies in her paintings are bodies of the late 20th century and the early 21st century. They are bodies which bear and bare the marks of the world we live in. In a way the world has caught up with Saville.

“When I was in Glasgow I did a painting called Plan which was to do with liposuction marks. I spent my whole time explaining what liposuction was.

“And there’s probably not a single person in the western world now who does not know what liposuction is, or Botox, or any of those things.

“When I first did a transgender body, people went: ‘What? Hermaphroditic bodies?’ And now there are so many in-between bodies that we all accept. It is fantastic that our culture has been able to accommodate that.

“The body is never going to leave us as a subject. It is our subject, because we are bodies.”

Now opens at Modern One in Edinburgh today.