Ms Versatility

Sitting on a plump, oversized sofa in the quiet of the library at the Soho Hotel in central London, Anna Maxwell Martin is telling me an embarrassing story. Having just finished a well-received run as Sally Bowles in Cabaret – quite a change from the earnest Esther Summerson in BBC1's award-winning adaptation of Bleak House – Martin was shopping in Waitrose when a woman caught her eye. "Oh it's you, it's you, isn't it? From Cabaret?" she says, deadpanning.

Martin, at 30, looks positively elfin. Maybe it's because her hair is cropped short. Maybe it's because she's pulled her legs up beneath her as she sips her peppermint tea. Either way, it fits perfectly with her self-deprecating humour and quick wit.

She speaks in an accent that bears only traces of East Yorkshire, where she grew up, and a great deal more of London, where she's lived for the past eight years. If the honour of being named the "next Judi Dench" by admirers brings a weighty responsibility, she seems to bear it with ease.

"They do that with a lot of people," she says of the accolade. "I'd love to emulate someone like Judi Dench but because we don't have a repertory system anymore it's very difficult to be as good as people like 'the Dame'. I wish I could go and play Lady Macbeth and Beatrice in the same season. But it doesn't happen these days and that means you're never going to be as good as they are, really. It's flattering to be compared but I'll never be able to touch her in terms of what she's done."

Comparisons to Dench may seem hyperbolic to Martin, but the fact is that she is a stunning actor. In a career that has already spanned TV (Bleak House), film (Becoming Jane) and stage (everything from The Little Foxes to Cabaret), she's picked up awards and nominations aplenty.

She brings an intensity to her performances that's quite at odds with how she is in person. Quick to laugh, she fizzes with energy, speaking fast, her accent wandering as she goes. She whizzes from how much she likes Scotland ("a lovely place"), to how much she'd like an allotment ("I'm so boring"), to the size of her "postage stamp" garden, in a matter of seconds.

Martin has lived in the capital since she arrived at the London Academy of Music and Drama (LAMDA) at the age of 21. She now lives in north London with her partner, film director Roger Michell. She craves the countryside.

She grew up in Beverley, East Yorkshire, the daughter of two scientists and younger sister to brother Adam. Her father was the managing director of a pharmaceutical company, her mother a research scientist. Childhood was happy and sheltered. At school she was a swot and although there was not a trace of thespian blood in her family, she was always a "drama queen"; but there were no weekly trips to the theatre or reciting or singing around the piano.

"There was nothing at all," she says. "I wish I could say I saw something that inspired me – Judi Dench or Ian McKellen – and I then thought, 'Oh, I want to act.' But I didn't. I was watching Cary Grant films and that was about it. I never wanted to do anything else other than act. Maybe I just like attention."

Nevertheless, she chose not to go straight to drama school, studying history instead at Liverpool University. So why, with the certainty that she wanted to act, did she delay? "It sounds like I was being very emotionally mature, but it really was a mixture of things," she says. "I don't know whether I knew I wasn't ready. Maybe I've said that in hindsight, to sound clever. I always maintained that I wanted to go to drama school from when I was really little but I come from a very academic family and I think I would have felt odd not going to university. I think there was also a sense that if you're going to do drama you need something to fall back on.

"It's not true. I mean, you can't fall back on a degree, anyway – you can't even get a job with a degree these days. It was what was expected of me and what I expected of myself."

As it was, after an inauspicious start at LAMDA ("I was just so lazy"), things picked up and when she was in her final year she landed a part in Lillian Hellman's The Little Foxes at the Donmar Warehouse. It was a particularly cherished achievement because it came in the year that her father was diagnosed with a rare cancer. "I can still remember acutely the feeling of being told I'd got that job," she says. "I was with my parents and my dad died shortly after that. For them to know that they had paid for me to go to drama school and it was OK ..."

And it certainly has been. The only quiet spell she has had since graduating was the period after Bleak House when she was sent nothing but costume dramas. "Part of the reason I became an actor is because I like doing lots of different things: different accents, different ages," she says. "That's what I've focused on. I've never been interested in playing the same roles all the time or playing anything like myself. I've always waited so that I can do things that I feel passionate about. I trained to be an actor so I want to use that."

Her newest role is another change. She plays N, a psychiatric patient in Channel 4's feature-length, darkly humorous drama Poppy Shakespeare, based on Clare Allan's award-winning novel of the same name. It's an astonishing performance.

"I read that part and I just thought, 'I can do something with this'," she says. "I 'get' her, what she's about. It was the same in White Girl (the provocative drama in BBC2's recent White season] – the foundations are all there to tell you why these women are the way they are, and I find that really interesting."

There's something about the performances Martin gives that lifts them beyond what we're used to seeing; a seriousness about the roles she picks, which she then excels at. She's less happy about the attention that has increasingly come her way as a result.

"The being on show, someone talking to you in the street, or being recognised, going to an awards thing where you have to have your photo taken, it's terribly uncomfortable," she says. "The people who act because they like all that – they love a premiere or whatever – well, they're not going to last very long. The reality is that if you're not in it because you love hanging around a set for 13 hours a day, or you love rehearsing for weeks on end, being torn apart by your director, then you might as well stop now."

Full of chat when we meet, Martin says that in bigger social situations she struggles. "I have battled with shyness," she says. "You have to get a grip in this business because you have to go to things all the time but there's no way on earth I could accept an invitation to something that I'd just have to turn up to on my own. I couldn't do it. It would kill me."

Martin is nothing if not contradictory. A self-confessed "prude" who happily cavorted as Sally Bowles ("you get used to it"), an extrovert who'd rather die than work her way round a room networking, super-critical of her own work but seldom interested in reading reviews, she's a compelling mix of self-consciousness and self-promotion, burning ambition tempered with Yorkshire humility.

"I didn't want to be an actor to be a film star. I wanted to be an actor to do all the plays I love," she says, before quickly adding: "And I'd quite like to be a film star. But I want to do everything. With film I do think that you've got to look a certain way and I don't really think that I fit that bill."

Her features have prompted the euphemisms "unconventional" and "interesting" in some quarters, and sometimes even less flattering descriptions.

"I don't think they're being mean, it's more that they're saying I don't have film star looks. And I think that's a good thing.

"I wouldn't change it. It does mean that Hollywood is not knocking on the door saying, 'Come over, come and be in a movie.' I'm not Keira Knightley, but I'm quite glad. It means that I've been able to play a 12-year-old on the stage, a single mum of three kids on a council estate, and someone on a psychiatric ward. I've been able to do lots of different things.

"But people do comment and it is weird. I don't know why. I'm obviously odd-looking."

In fact, Martin isn't odd-looking at all. She's pretty. She has piercing blue eyes, a petite nose and the kind of smile that completely lights up her face.

Confident enough in her ability in terms of her career, she's happy not to plan too much. "It's weird, because I really did have a plan when I left drama school," she says. "I had my pipe dreams. They were the Donmar, the National, the Almeida and the Court. And I've managed to do all of them.

"I think I'm in a funny position with work. I don't really know what will come next because I'm not going to head off to Hollywood, I'm not going to do that."

But would she really want to go to Los Angeles and make movies?

"I wouldn't want to go out there and tout myself around but if something came up..." she trails off. "I've been close a couple of times when it's been between me and someone else and they've got it. That's happened twice and I sort of think, well, if it happens it happens, and that would be great, but I'm not going to move out there for six months and try and work it because it's clear I can't."

And no sooner is that low note sounded before mercurial Anna returns. "I don't feel that I've got to this age and I've not proved myself yet. I've done some good work. I've proved myself a bit and I've got loads more to show. If I'm lucky enough to get the parts I'll be able to do that."

Poppy Shakespeare is broadcast on Monday on Channel 4 at 9pm.