Sally Hawkins: 'You only do good work when you're taking risks'

"Woody is still a complete enigma to me. I adore him," the actress Sally Hawkins tells me. "He's incredibly complex but brilliant. At 76, he's just perpetual forward motion. He's so different to other directors, he's very free. He has the words – yet he wants them to fit your mouth."

Hawkins, aged 36, is just back in London after shooting Woody Allen's new, as yet untitled film in New York and San Francisco. It's her second outing with Allen – she played Colin Farrell's wife in Cassandra's Dream – but this time she has a lead role as Cate Blanchett's sister. Allen has described the new film as a "serious piece" rather than a comedy.

"I hope there are funny moments," says Hawkins, "but it's quite a tragic story. There wasn't much time before filming, but Cate and I had conversations about where the characters grew up so we could anchor it for ourselves. We play adopted sisters, so we could be connected but without much of a familiarity with each other. My character moved away quite young, so they are slightly like strangers and yet know each other so well."

She's forbidden to say much about the plot but insists Allen is the exact opposite of a controlling director. "If something isn't working in a scene, he'll take it on himself. It doesn't cross his mind that it could be the actor! But he has a complete overview of the film's structure: he'll tell you how the audience will already have got bored by that point and moved on, and how we need to hit that beat. He has it all in here," she says tapping her forehead.

In between scenes, he'll disappear into a meditative space: "he has those little moments where he goes somewhere in his head".

She has high praise, too, for Blanchett. "She's a proper actress, whatever that means. I had huge respect before meeting her and slight intimidation – I've watched her for so many years. She's incredibly clever and really in it for the right reasons, that's obvious every time she opens her mouth on screen. She loves it – she loves the word."

But then the same is true of Hawkins. After her role in Mike Leigh's Happy-Go-Lucky, as Poppy the effervescent primary-school teacher (which won her the 2008 Best Actress Golden Globe) and Made in Dagenham, which told the story of the 1968 women's strike at the Ford car works, Hollywood sat up and took notice.

These days she's as likely to be filming in San Francisco as Camden. And yet, when I meet Hawkins, at the Young Vic theatre café in south London, she still looks about 14, dressed in a white jumper with gold stripes and jeans. With her translucent skin and deep-set hazel eyes, she's dream-casting for period drama. And yet she relishes contemporary roles.

Hawkins is renowned for avoiding the spotlight. Her role model is Judi Dench, who is passionate about the work but "disappears" in between roles. But for all the shyness, there's an earthiness to the actress. Leigh cast her against type as a fabulously sexy bitch in his film All or Nothing. "It was so liberating. Normally I'm the sweet little thing."

Then followed the role of a gangster's moll in Layer Cake and Sue in Fingersmith, based on the Sarah Waters novel. The sex scenes were exquisitely done – just a flash of stomach – but many people still swear both actresses were topless. Sex is to do with the mind, she argues.

She's made three films this year. There's a cameo role in Mike Newell's Great Expectations as Mrs Joe, Pip's terrifying older sister ("she's quite loud, probably shouting across the Moors hasn't helped") and last spring she shot indie film, Lucky Dog, opposite Paul Rudd and Paul Giamatti, about two French-Canadian Christmas tree salesmen who travel to New York.

It's directed by Phil Morrison who made the 2005 American comedy-drama Junebug (which won Amy Adams a Best Supporting Actress nomination). Hawkins is the Russian housekeeper, Olga, who befriends Giamatti. "It's heartbreaking, he's out of prison, trying to get straight, and ends up selling Christmas trees illegally on a tiny patch of dirt in Brooklyn. Olga befriends him. It's a film where nothing happens – and everything happens."

In the film, Olga is a pianist. Fortunately, Hawkins plays in real life. "It was a lovely excuse to re-learn. I fell in love with classical piano again; nothing gets me like piano solos." She often uses music to prepare for a role. "I love Bach, and the designer on The House of Bernarda Alba at the National gave me the Goldberg Variations, which changed everything. It can also just help you get up in the morning."

For all the fragility, there is something immensely practical about Hawkins. She learnt to sew for her role as machinist Rita O'Grady, the leader of the walk-out in Made in Dagenham (Hawkins' own grandmother was a machinist).

She's also spent this year boning up on quantum physics for her new play Constellations, a 70-minute two-hander with Rafe Spall, which has just transferred to the West End.

When it first opened at the Royal Court's tiny theatre upstairs in January, the play – performed on a simple raised platform under a night sky of white balloons – won five-star reviews.

The Telegraph declared it "pitch-perfect", singling out Hawkins' "glowing humanity and deep poignancy". The Independent's theatre critic, Paul Taylor, called it "a wonderful achievement", performed with "uncanny brilliance" by Hawkins and Spall.

Written by twentysomething playwright, Nick Payne, it's a love story with a difference. High-concept scientist Marianne (Hawkins) meets beekeeper Roland (Spall) at a barbecue.

In dizzying succession, they act out all the possible scenarios of a love affair: he's not interested, she's too clingy; he's married, she's bored; they're ecstatically in love, he betrays her.

Scenes are constantly replayed with different endings, suggesting there are many parallel universes, as Payne uses advanced physics as a metaphor for life. It's fiendishly difficult to learn, Hawkins admits. "It's a lifetime packed into this ball of a play. But the writing's so clever, it hooks you. Nick manages to anchor these huge intellectual concepts in the very mundane and everyday."

Funny and sexy and tender, Constellations is also shot through with pain. Marianne has occasional symptoms of a neurological disorder. She is literally losing her language. In the programme credits, Payne explains he drew on the writings of Tom Lubbock, The Independent's much-loved art critic who died of a brain tumour last year.

"It's quite heartbreaking doing those scenes again," Hawkins admits. She has the last-ever piece Lubbock wrote about his illness pinned to her mirror during performances.

Hawkins has to trust Spall implicitly on stage. "Because it's so intimate, you're eyeballing each other all night. The play moves at such a pace, you need to be with someone you love as a person. Thank God it's Rafe. He's so generous, f and exactly the type of man you want to be on stage with. He's kind and wise and very charismatic, like his dad Timothy Spall." As if on cue, Spall Jnr waves through the window of the café.

In person, Hawkins is as delightful as you'd hope, but she obviously loathes interviews. "I just worry that I'll disappoint. I get tongue-tied and self-conscious." It's a measure of her passion for Payne's play that she's talking to me now. "He's got such a voice for someone so young. It makes you work your muscles as an actor."

It's interesting that she talks so much about language and verbal dexterity, because Hawkins is dyslexic. As a child, she stammered and found it hard to look people in the eye. These days, she's learnt to live with it, though sight-reading is terrifying.

Her parents are the children's book illustrators and writers, Jacqui and Colin Hawkins; her older brother is a web designer and illustrator. She grew up in Blackheath in an elegant "gingerbread house", designed by 1950s architect Patrick Gwynne, and protected by the National Trust. Her parents' studio was full of puppets, pirate ships and spooky monsters – to inspire their books. She went to James Allen's Girls' School in Dulwich.

Discovering acting changed everything. "Something clicked. English was always an academic subject, there was a barrier I found so hard to break. But as soon as I spoke the words, I understood what they meant. This whole world of literature unlocked, which I'd been scared of." Interestingly, her illustrator father often acts out a character's part before he draws it, to test the dialogue.

She was accepted by Rada, and when she graduated in 1998, her "brilliantly organised" friend, the actress Maxine Peake, sent out their joint CVs.

They met Leigh's casting director, Nina Gold, who took Hawkins to meet Leigh at his Soho office, where he spent an hour chatting about her hobbies, inspirations and dreams.

Later on, Leigh built the whole role of Poppy around her "energy, humour and profundity". You commit to a six-month rehearsal period before Leigh shoots. "I don't know how else to put this – but he's sort of plugging into your brain and sucking out everything that he needs: very detailed notes."

Although she is often cast in serious roles, she says it was refreshing to be free to make jokes and be naughty and mischievous, and not be told off for it.

You sense an endearing silliness: she played Kenny Craig's girlfriend in Little Britain (in one famous episode David Walliams vomited on her). She has also written sketches for Radio 4's Concrete Cow.

Having worked with Woody Allen twice now, she says he overlaps with Leigh, even though they appear to be at opposite ends of the scale. "Mike is inside out, and Woody is outside in – he just wants you to turn up and be it. But they both take elements from the actors themselves and use any strengths."

After Happy-Go-Lucky, she was offered a few Bruce Willis blockbusters but held out against them. Her heroes are the filmmakers Robert Altman and John Cassavetes. "You only do good work when you're taking risks and pushing yourself; and failing really badly," she laughs.

She protects her private life. At home she loves gardening and plants: "being in nature is very important to me". And you sense her red-carpet appearances have left her slightly uncomfortable. "I'm not a glamour puss."

She also admits that it gets lonely filming: "You know it's not for ever, you'll be home soon, but you do miss just being able to hug your family and friends. If I had children that would be a different matter. I'm quite lucky in the way I have that freedom." Is it still easier for men? "Very much."

She and her friend James Corden (her co-star in Leigh's All or Nothing) narrowly missed meeting in New York, where he was doing One Man, Two Guvnors. "I know James will be busy for the rest of time if he's got anything to do with it. He's very good at managing it, but also effortlessly social; I don't know how he does it," she grins.

Hawkins tries to stay physically fit for the "marathon" of filming. "It's about stamina, making sure you're the best you can be, trying to get as much sleep as possible, so you can serve the script and the character, and be open to what the director wants. You need to be on top of your game, so you can react to the surprising things that could trip you up. I find it very interesting reading about how athletes work and train."

She's also a huge fan of the choreographer Pina Bausch. "We're all dancers, and knowing how to use body language is important. It gives you another way in, and can unlock strong emotions." At drama school she studied Laban Movement Analysis, a method that describes and documents human movement. "Physical memory helps. It can be so cerebral but unless you know it in your body it won't make sense."

The thing she loves about acting is she can enter into these other people's lives. "But going back to being me at the end of the day is very important, too… I do worry about young people in the business who have experienced a lot of success and are punted around doing those manic publicity trails, when you don't really know who you are yet."

She's mostly acting in an American accent these days but describes it as "like a coat, part of the costume". She's still the girl from Blackheath. "I would hate to lose that Englishness. The one thing that's going to get you through this business is having strong roots, being grounded and knowing what is true."

'Constellations' is at the Duke of York's Theatre, London WC2, 020-7565 6500, royalcourtatdukes.com