In the 1970s, through 1980, the photographer Francesca Woodman made images of young women, most often herself, in a blurry, foggy, subliminal state. She called one famous series her ghost pictures. They were achieved through slow shutter speeds, which meant that instead of being the record of a blinked instant, they captured movement through time and mid-air: in one a female figure leans forward, body flexed, awkward, in fizzing focus, while her head shakes frantically, blurrily, as if ridding herself of a wasp. Many of the figures are almost transparent. I am here, they insist. But watch me disappear.

When Carey Mulligan was working on her latest film, Shame, she saw a documentary about the Woodman family and Francesca's work inspired her character Sissy – a damaged, needy, tinnily upbeat young woman, whose singing act becomes her last desperate attempt to forge a relationship with her brother. When she is working on a film, says Mulligan, she often makes scrapbooks for her character. "It really is so childish. It's like my way of saying," – she puts on a child's voice – "'I'm qualified!' ... I had little Woodman pictures in the book, stuff like that." Her voice goes quiet. "If anyone ever read them I'd be mortified because they're just full of shit. They're not clever and there's nothing creative in them. It's just me reassuring myself."

Mulligan with Peter Sarsgaard in An Education.

Mulligan's conversation veers between supreme confidence – her willingness to argue openly, straightforwardly, to secure the jobs she wants – and serious self-effacement. When I look at Woodman's photographs after the interview, they remind me of Mulligan, not in their angst (the photographer killed herself at 22), but in their depiction of a young woman suspended in an odd, disconcerting moment. In Mulligan's case, this began with the release of her 2009 film An Education – one of her first leading roles – and continued through her 2010 Oscar nomination for best actress. She went overnight from normal life to 50ft-billboard fame. And although she appreciates her circumstances, she still seems to be absorbing them. "Sometimes it's so weird just to do an interview," she says. "This morning I was back in my parents' house, with my brother, and we went for a jog together, then had breakfast as a family. And a couple of hours later I'm wearing high heels and a dress and makeup, and talking about my job. It's such a strange reality – and a wonderful one."

We meet a few days after a screening of Shame, a dark, powerful film by the artist and director Steve McQueen, starring Michael Fassbender as Brandon, a young professional living in New York who is addicted to sex. The film strips the subject of prurience, so it becomes like any addiction – an action that has moved from habit to horror; never pleasurable, always functional; a repetitive reaction to grief. There are clues to Brandon's unhappiness in his relationship with Mulligan's character Sissy, who turns up unexpectedly at his flat. "We're not bad people," she reassures him in the film's most direct line. "We just come from a bad place."

Mulligan was desperate for the role, and says she agreed with McQueen when he told her: "You're good, but if you're going to do this you're going to have to be 16 times better." Their first interview to discuss her taking the part didn't start well. "He tried to leave about 10 minutes in," she says, "when I was there to basically beg for the job, an audition, whatever. He was like," – she half stands, holding out an arm to leave – "'All right, nice to meet you,' and I was like, 'WOAH! Wo, wo, wo – what are you doing?' So I convinced him to sit down again, and he started asking why I wanted the part, and I basically said I just hadn't found a film role comparable to how I felt when I was playing Nina in The Seagull." Mulligan played the ambitious, troubled Nina to enormous acclaim at the Royal Court in 2007, before transferring to Broadway. "And when I read this script I thought, it's not the same person, but I hadn't found that sort of fear in anything for a while ... So I said: 'This is exactly the kind of film I want to be making. I don't want to be making big, silly films.' And then – Oh God, I was really trying to get the job – I started reciting Chekhov. I started going," – she babbles these words: "'I know now, I understand, it's not about fame or glory, all the things I used to dream about, it's the ability to endure, to bear your cross, to keep the faith, I do have faith, and when I think about my vocation, I'm not afraid of life.' And he said: 'That's right! You're an artist!' And I said, 'I know!'

"He got me so riled up I said: 'In fact, I want to get a tattoo of that just to remind myself.' And he said: 'You get the tattoo, you get the job.' The next day I did, and he gave me the job that afternoon." I ask to see the tattoo, and she holds out her right wrist. Inside is a small, delicate outline of a seagull. "But, and this is awful, I thought, I can't walk into a Soho tattoo parlour, because I'm so ridiculously middle class, and not cool, so I need a place where I can go and not feel like a total idiot. And it was Selfridges. And actually I felt like more of an idiot there."

With Michael Fassbender in Shame.

She leans forward on the sofa, touching her toes, as she does often in the interview. It is at odds with her elegant black dress, but fits her age – she's 26 – and friendly demeanour.

The first time we see Sissy is when she's confronted in the shower by Brandon; she doesn't grab a towel, but stands there naked, talking. Through the film they argue and bicker, the tension rising. In one of the most striking scenes, she performs a slowed-down, stripped-back version of New York – New York in a bar; a sad, psychological hymn to where their lives have brought them. Sissy's arms are streaked with scars, and while Mulligan did some online research into people who self-harm, she says she didn't talk to anyone in person, because "I don't think you should ever damage other people for your art." When she started out in acting, she always tried to draw on her own experiences, but stopped when she appeared as Nina, "who runs away to Moscow, has a child and loses the baby, all of that. I was working with Ian Rickson, and he taught me to invent in a way I hadn't been. With Sissy, I could never draw from my life." Because she hasn't had those experiences? "No! Thank the lord."

She found every aspect of the role daunting, because Sissy is "such an exhibitionist, such an extrovert. I tend to clamp up on camera, but this meant working with no inhibitions. I mean, I don't wear a bikini on the beach. I walk around my house in pyjamas. I haven't seen myself naked in the mirror for probably a decade. I'm very prudish."

So her family doesn't walk around naked? "No, no, no, no, no, no," she says. "I would scream if I saw any of my family naked, and vice versa." But the way the film was shot made her feel comfortable. Before filming started, she was living in New York, and "hanging out with friends. And when I got the job I just felt that she wasn't someone who works out. I was living it up, eating what I liked. I accepted I wasn't trying to look great, and that was the reason I felt so comfortable, because the way it was shot meant [the nudity] was anatomical, not sexual." When her best friend saw the film, she says, he told her the character was like her "in extremis, at my absolute worst ... My best friend has seen me horribly drunk before, and I'm sure I've behaved badly in front of him, and she was me if I had none of these good people around me, and had gone down the wrong track. Obviously I hope I'd never end up like her, because she doesn't have any boundaries. Whereas I'm more the sort of person who doesn't like hugging strangers because we don't know each other, so we shouldn't." What about kissing on each cheek? "I always fuck it up. I just like a good old handshake."

Mulligan grew up in hotels; her father was a highly successful hotel manager, and she was born in Mayfair, before moving with her parents and older brother to Hyde Park Corner, then on to Hanover in Germany, and Düsseldorf. She wanted to be an actor since she was small, and her first ambition was to appear in musicals. "Then I realised, at 14, that you have to be able to sing really loudly, and really well, and I can't dance to save my life."

While studying for her A-levels at Woldingham, a private school for girls, she applied for drama school in secret. Her parents had said she should go to university first. She was outraged, so put down three drama schools on her UCAS form. There was a "movie story in my head", she says, that "against all the odds I'd get in, and I'd be like," – she crows in mock-triumph – "'Ha, Mum and Dad – look! My talent has been recognised! You must recognise it too!'" All the drama schools rejected her. Did she consider giving up? "No. I just knew I had to try to do it." The experience didn't dent her confidence, she says, "because I didn't think I was very good. I just imagined that I could be good, or would like to be."

The screenwriter Julian Fellowes had given a talk at her school, and so she contacted him, explaining how much she wanted to act. He and his wife helped her get an audition for a film version of Pride and Prejudice, she won the part and was soon appearing at the Royal Court, and in Bleak House, then as Jenny in An Education. Playing a 16-year-old in a stifling suburban home in the early 60s, trying to escape through a relationship with a seductive, secretive older man, Mulligan caught the knowingness and vulnerability of her character perfectly – her excitement at moving up and away from her parents' stultifying world, and the wrench of that too. Her pixie-ish features won comparisons with Audrey Hepburn, while the slight downward slope of her eyes conveyed muted sadness.

Mulligan with Tobey Maguire and Leonardo DiCaprio in The Great Gatsby. Photograph: Planet Photos

She had expected the film to be shown in small arthouse cinemas, had no idea it would even be distributed in the US, so when her Oscar nomination was announced she was shocked. "I was like a rabbit in the headlights, and went through the whole awards season hiding behind Colin Firth," who was nominated for best actor for A Single Man. The two actors share a publicist, and they would go to events together, "and I'd be like," – she clenches her teeth – "'I don't want to meet anyone famous,' and he'd say: 'You don't have to.' Him and his wife looked after me.

"We went to a party once, full of industry people, and went into the corner and were basically the only two British people there. We created a circle of hostility, so no one would try and talk to us, and we didn't have to talk to anyone. There were five of us, all cowering, and we drank our wine, and would occasionally stare out intimidatingly, to keep people away. Not because people were clawing to talk to me," she adds quickly, "although they were probably clawing to talk to Colin – but it's very strange. I felt like the person who had accidentally been invited to the party."

She won't talk about her private life – when I ask whether she's engaged to the musician Marcus Mumford, as has been reported, she says: "I'm not going to answer that!" and then mock-screams and says she finds it odd being written about. "I really try not to read anything [online], and then occasionally I will be completely self-destructive, once every six months, and it's really horrible. Sometimes people write the most ghastly things, and it makes you feel like crap ... A while ago I read some stuff, and it was tonnes of people, all saying I wasn't beautiful enough to be an actress. And I thought, well," she sounds crestfallen, "that's not what you're meant to be. I've never aspired to play a character that was beautiful."

The closest exception, she admits, is the wealthy, rarefied Daisy Buchanan in The Great Gatsby – a role she's been filming in Sydney with co-star Leonardo DiCaprio and director Baz Luhrmann. She was at an event when she found out she'd landed the role; Luhrmann's wife, Catherine Martin, was there, handed her the phone, and, "It was Baz," says Mulligan, "and he was going," she puts on a deep Australian accent, "'Hello Daisy'. And I was crying, and people were milling around, and I was sobbing and couldn't talk." She says she's been freaking out every day of filming, because "it's so tricky to make sure she doesn't become one-noted, or too emotional. I'm balancing it all, and terrified of messing it up."

The role looks likely to push her to another level of fame, into another strange bubble. Does she want to disappear into her roles? "I can walk down the street and nobody ever recognises me," she says, "so I'm pleased to be in that category of disappearing into things. Sometimes someone will come up and say, 'Are you Auntie Suzie's girl?' because they think I'm related to them. And I can just say no, and walk away."