Saffron Burrows can barely contain herself. “It's so exciting! Everywhere you look there's some sort of trade union action!” says the 35-year-old actress, cooing enthusiastically about the recent politicisation of Hollywood. “In the middle of town there's a big anti-war demonstration, and in Beverly Hills there's a sign saying, 'Shame on You Four Seasons Hotel: Industrial Action Taking Place Here.' It's been kind of extraordinary since the writers' strike. Around every corner there's a banner of some kind.”

Burrows, you see, doesn't do trivial. Fiercely intelligent, beautifully aloof and a self-declared socialist, the star from Hackney, East London, of the blockbusters Troy and Deep Blue Sea, and the indies Miss Julie and Timecode, has always reserved the right to be different. Other actresses swear by Balenciaga, Pilates and proteinenriched diets. Burrows has Trotsky, Beckett and Yeats on her side. No, really. For her new film, The Bank Job, a cheeky “cockerney” crime caper set in London in 1971 and written by the comedy veterans Dick Clement and Ian La Frenais (Porridge), Burrows found her inspiration in the soul of Samuel Beckett's Happy Days. Her role, she says, as Martine the mobster contact who initiates the robbery, has much in common with Beckett's immobile protagonist.

“The alienation that Winnie feels in Happy Days, which is a certain peculiarity that I've witnessed in the British Isles, and which is about people getting stuck in a life that they don't want to be in, is happening not just to mine, but to several characters in The Bank Job.” She says this without irony or lofty condescension, but with the casual intellectual élan of someone who is conversant in Big Ideas. Burrows adds that she is never cynical about her roles, from Circle of Friends right up to the Adam Sandler melodrama Reign Over Me, but that recently she has started to approach her characters differently. She now explores what's churning around inside them, rather than keeping a cool “anthropological” distance.

She calls this stage of her career, her “proactive” phase. She is based partly in London and partly in LA, where she shoots her primetime TV series Boston Legal - she plays the show's knockout attorney Lorraine Weller. “When I was a young enthusiastic actor every job seemed like a miracle,” she says. “But as you get more experienced you focus more and hone your tastes. You become more proactive.” She adds, too, that it helps now to be at a certain age where the roles become richer and more fully fleshed, such as the career high turn she's just given as a woman with throat cancer in The Guitar, the directing debut of Amy Redford (daughter of Robert). The film was a smash at Sundance, and fully confirmed the often underappreciated notion that in Burrows there is an actress of screen-chewing intensity.

In the past, of course, it was different. She seemed to exist in a rarefied air of lonely but enigmatic beauty. Whether drifting past Daniel Day- Lewis in Jim Sheridan's In the Name of the Father, or taking centre stage in Mike Figgis's Miss Julie, she could draw you inexorably into her web, yet at the last minute she'd let the cold magic of her smooth, impassive features hold you back (maybe it was that “anthropological” approach?). It didn't help that she had been a model, and was tagged as such in the narrow minds of tastemakers.

Dimple-chinned and bean-pole tall (she is a lean 6ft), she was discovered at 15 in Covent Garden by the modelling agent Beth Boldt (the women who “found” Naomi Campbell). She was shopping with her mother and younger brother when Boldt approached. Burrows's parents were both teachers and trade union activists, and they had sent her out on to the streets of Hackney to sell Socialist Worker (hence, the love of Trotsky). She says that she was terrified by the prospect of modelling, but nonetheless she appeared at Boldt's office and was immediately sent to live in Paris, where she became a regular fixture on the catwalks of Chanel and Yves St Laurent.

She says that, on reflection, it was a monumental change, and hugely significant for who she was to become. “I was thrust into that world, probably too young,” she says. “And so I carried around books with me as if they were friends to protect me.” It was then, you imagine, that the self-creation of Saffron Burrows began in earnest. And soon the books, the intellectualism, the socialism, the sophistication and the traffic-stopping beauty all emerged from the Paris years to appear on the big screen as a mass of beguiling contradictions.

Thus we thrilled when this so-called model spoke, in that throaty caramel rush of RP vowels and occasional glottal stops, about her childhood friendship with the socialist politician Tony Benn. Her love life, too, corroborated her sense of mystery. Day-Lewis had fallen for her, as did Figgis, for whom she became a muse (he made four movies with her). She was even engaged to the actor and zany Scottish sprite Alan Cumming. When their relationship ended, Cumming announced, rather ungallantly, that Saffron “bats for both teams”.

This “revelation”, however, neither denied nor confirmed, only deepened the Burrows enigma. And certainly today she has no interest in shattering that myth. “For many reasons, I'd rather talk about the work,” she says.

And the work is where we end, and where she is now, acting her heart out in Redford's The Guitar. She says that there is so much to discuss about the movie. That she can't wait for me to see it. And that she is exposed, intellectually and physically throughout. She repeats again that she can't wait for me to see it, and, as I agree, I can only imagine Burrows the actress exposed, just as I can only hope that some of the enigma remains.

The Bank Job is out on Thur, and will be reviewed in The Times the same day; Boston Legal, Living, Thur, 10pm

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