While she may have played Leonardo DiCaprio's colleague in The Beach, one only has to look at Swinton's vanity-free past performances to know that she is the very antithesis to the blonde, bland starlets that decorate studio fare. How many would have dared play her gender-bending role in Sally Potter's Orlando, or followed it with the repugnant Colony Club bartender Muriel Belcher in the Francis Bacon tale Love is the Devil and the hairy-legged barge-owner in Young Adam?
In this month's Jim Jarmusch movie Broken Flowers, she is almost unrecognisable as a raven-haired biker chick - a former flame to Bill Murray's middle-aged man-in-crisis, and looking like the love-child of Joan Jett and Ozzy Osbourne. It should be perfect training for her forthcoming role as the Velvet Underground collaborator and heroin addict Nico, for which Swinton - who turns 45 soon - will age from 22 to 50. As Bill Murray notes, "If you spent a week with Tilda Swinton, you'd have so much information. She is alive and is not wasting a moment."
Cambridge-educated - she read social and political sciences - her interest is more in the world around her than the self-absorbed universe occupied by many of her peers. After graduating in 1983, Swinton joined the Royal Shakespeare Company but left it after one season. She compared it to what she imagined working for the industrial giant ICI would be like. "I'm not gregarious enough to enjoy working in the theatre," she says. "I'm not interested in acting or actors. I'm largely in films because I love the way it's all done with mirrors. I'm a scientist. That's my interest."
The latest love of her life, cinematically speaking, is Mike Mills, whose varied work includes designing album covers for Sonic Youth and shooting promos for Air. Mills is well aware that he owes a great deal to Swinton for her commitment to the project while he tried to secure financing. "As soon as Tilda was on board, it made it safe for other people," he says. Based on the novel by Walter Kirn, Thumbsucker sees Swinton play Audrey Cobb, the wife of D'Onofrio's failed pro-sports star Mike. Together they are parents of Justin (Lou Taylor Pucci), a traumatised teen who still sucks his thumb for comfort. Audrey seeks relief by obsessing over a hunky soap-star (played by Benjamin Bratt).
"There's something radical about a coming-of-age story that's about everyone trying to come of age at the same time," says Swinton. "It's not so much about growing up as growing on. There's something compassionate about parents not knowing what they're doing."
The partner of the playwright John Byrne, and the mother of their seven year-old twins Xavier and Honor, Swinton - who received a Golden Globe nomination for her previous mother-figure, in 2001's The Deep End - admits that making the film helped her to think about her own family. "It made it really clear to me that not only is it impossible to communicate with one's family beyond any kind of grunt, but also highlighted the way in which, in families, one finds oneself very often saying about somebody else what one wants to say about oneself. So Justin says about Audrey, 'She's not happy' - just as we've seen him being unhappy. One projects so clearly onto other members of one's family. Everybody looks like a mirror-image of oneself. Certainly that's my experience - everybody looks like me in my family anyway, so it doesn't help.
"The whole idea that one is alone in the world is really hard to take. I see my seven-year-olds coping with it, and they're twins, so they have an extra situation to deal with. And it's moving. It's really, profoundly humbling to be around; it's a serious situation for them. But at least they're honest enough to scream all the way home, in the car. It's what we'd all like to do sometimes - or stick our thumb in our mouths." So how does she cope with such existential angst? "I scream all the way home in the car - or make films," she replies. "But I do know that it's all right to be lonely, and everybody's lonely."
Being the daughter of a Scottish major-general and an alumna of Princess Diana's boarding school, West Heath, has given an almost military precision to Swinton's vowel sounds. She travelled extensively as a child when her father, a former commander of the Household Division, was posted across the globe. After university, in Edinburgh in the mid-1980s, she met Derek Jarman when he cast her as the prostitute Lena in his 1986 film Caravaggio. They would go on to collaborate on another six films before he died.
"It was eight years of a very important friendship, and the beginning of me making films. It has stars on it by the calendar! I can't ever stop being grateful for the luck of meeting him, and working with him. It's possible that if I hadn't met him, I wouldn't be able to be working in films. What I was able to learn from him, in a safe enclosure, was the science of making films."
Based now in Easter Ross in the Highlands, Swinton has no intention of packing her bags for Hollywood. "To go home to Scotland is such a privilege," she says. "I'm too lazy to be very controlling. I believe in laziness. But I really like making films, and I feel very peaceful in front of a camera."
'Broken Flowers' opens on 21 October. 'Thumbsucker' is released on 28 October and 'The Chronicles of Narnia' on 8 December