'Good night," says Sally Hawkins, before catching herself. "If only," she sighs. It's early afternoon. Yesterday she was on Broadway playing Tony award-winner Cherry Jones's daughter in Shaw's Mrs Warren's Profession. She's come directly from Heathrow to talk about Made in Dagenham in which she plays the leader of a group of women machinists at a Ford factory whose strike led to the introduction in British law of an Equal Pay Act in 1970. Tomorrow she'll be back on Broadway. "I'm red-eyed," she apologises.

There's a girl-next-door friendliness that shines through whatever role she plays. A diminutive figure with long black hair and a curly fringe, she talks in a rush as if thinking out loud. "The people I admire are the people who go through life with a smile," she says. Like her character Rita O'Grady in Made in Dagenham – who turns out not to be the pushover condescending male union officials, bosses and politicians assume – her openness is a strength rather than a weakness.

"I hadn't heard about the Dagenham women until I read an early draft of the script. They were instrumental in making history. Without them God knows where we'd be. But there are a lot of women like that, ones that we know and ones that we don't. They're all important." So has she ever – like these women – dared to do what she never thought she would? "Every day," she laughs. "I'm lucky acting has taken me places I'd never have dreamt of. I never know what I'm doing from one moment to the next. It's always a surprise. Sometimes it's brilliant and everyone wants to talk with you and is interested in your work but then the next thing nobody is."

When she heard her name read out at the Golden Globes in Los Angeles two years ago as best actress for her performance as Poppy, the giddily funny L-driver who radiates a zany optimism in Mike Leigh's Happy-Go-Lucky, she couldn't wait to get back to her home in Richmond, London. "That's not my scene," she says. "I'm not really Hollywood material."

Tell that to Broadway. Mrs Warren's Profession began previews on 3 September for its 3 October opening but already internet bloggers are acclaiming her performance as "the greatest acting job in a long time".

Her parents Jacqui and Colin were art teachers who hit on the idea of making children's books to encourage her to read when they discovered she was dyslexic. Their first book Witches was published in 1981 when she was five and they've gone on to create such popular works as Tog the Dog, Terrible Terrible Tiger, and Foxy and Friends Go Racing, the characters of which became a weekly TV series. "I was lucky they valued creativity and self-expression. When I was little I loved drawing and painting, and I loved stories."

She started acting at primary school at Dulwich in southeast London. Suddenly she wasn't shy any more. "That was the way creativity came about for me. But for a long time I didn't know whether I wanted to do art or theatre. You had to choose one or the other so I took theatre and went to Rada. But I still paint and write. I know I'll pick it up again whenever I need to. The way I chill out is going to an art gallery on my own. That really relaxes me."

She found an agent at Rada who brought her to the attention of Mike Leigh. Her spontaneity made her a natural for his improvisational style of filming. He gave her small parts in All or Nothing and Vera Drake before the lead in Happy-Go-Lucky. With Leigh she found the freedom to be truly creative. "When you go into work with him you don't have a script. You build your character's life from scratch with Mike guiding you. That's why his films are always so rich."

Working with Woody Allen in Cassandra's Dream was more constrained. Unlike his normal approach in which actors are encouraged to improvise, the thriller format required everyone to stick to their lines. "I had a script and we didn't really deviate from that." But co-starring with Colin Farrell made it all worthwhile. "He's beautiful. I just love him. He's a very good friend now, which is a lovely thing to say. I was quite starstruck when I met him because he's Colin Farrell. But he's a most generous man and so bright and so passionate about what he does. He works hard and all he cares about is doing a good job. I worried about meeting him because he had this persona in the press that is so not like the man he is. I was gobsmacked."

Hawkins co-stars with Keira Knightley and Carey Mulligan in Never Let Me Go, which opens London Film Festival on 15 October. Adapted from the Kazuo Ishiguro novel, she plays a teacher at a school for children cloned to be organ donors. And this summer she filmed a new version of Jane Eyre, in which Michael Fassbender plays Rochester. "Sadly we never meet. I play the aunt to the young Jane Eyre."

Her next role could be Bernadette Devlin in The Roaring Girl, a biopic announced at Cannes Festival. "It would be a gift of a part. It's a huge responsibility not only to Bernadette but to Irish history. I just hope it happens and that I'm up to it when it does."

'Made in Dagenham' opens Friday