Joan Allen sits in the kitchen of her New York apartment like a debutante getting ready for her big coming-out ball. Dressed in casual shorts and T-shirt, she perches on a stool while a stylist fusses with her hair and make-up. She clutches her pocket-sized Boston terrier, Nora, to her - a fixed, calm point in a blur of bustle and excitement. More stylists and photographers' assistants trot in and out, walking fast and talking even faster, all in preparation for a photoshoot with InStyle magazine, a fashion and celebrity glossy. Allen slips on her sandals, and suggests that we go outside to talk in a restaurant instead. Downstairs, big men are unloading a buffet of avocado salad, rolls, satays and chocolate mousse on to the pavement, but Allen strides by as if none of this has anything to do with her.

Allen is handsome and high-cheekboned, but on the street nobody recognises her. She has appeared in more than 30 films and been nominated three times for an Oscar, and yet she has one of those faces that is hard to place. But if you've seen Nixon, The Crucible or The Contender - the three films for which she was Oscar-nominated - the penny would drop without touching the sides. Until recently she has tended to play supporting roles, a brittle pillar for flawed yet forceful men: Pat Nixon, Elizabeth Proctor in The Crucible, Bonnie Waitzkin in Searching For Bobby Fischer. She's a wife again in Pleasantville, a suburban ice maiden who blossoms.

Now, Allen, 48, has ditched the celluloid husbands and started doing her own thing. She was the contender - a would-be US vice-president - in The Contender; she made a steely CIA boss in The Bourne Supremacy. In her latest film, Yes, directed by Sally Potter (who directed Tilda Swinton in Orlando), Allen finally gets to let down her hair in a sensuous, sexy role. She stars as a lonely woman in a loveless marriage who has an affair with a Lebanese man in London. Cast simply as "She", Allen plays an Irish-American scientist, while Simon Abkarian, playing the Lebanese surgeon turned cook, is known only as "He". The film charts the course of an affair that crashes on the rocks of the pair's cultural and ethnic differences, only to wash up smelling of hope on the shores of Cuba. Oh, and the whole thing is in verse.

Allen admits to feeling a little anxious when she got the script. "I was a bit intimidated by the verse. I thought, 'Can I pull this off? I don't know.'" Her main reason for trying was that Potter was the director. "I liked Sally so much that if it's something she's doing then I've got to meet with her; I've got to talk to her about this, because I loved the story." Indeed, the subtext to the film seems to be a secondary love story between Potter and Allen. Potter has said she thought Allen was sensuous; Allen says she found Potter almost maternal. "I felt so nurtured with her. She said, 'I will not put one frame in this film where you do not look exquisite.' I've never had a director say that before."

Potter is the first woman director she has worked with. "That's sad, isn't it?" she says. "But Sally is unique regardless of her gender. Other film directors would maybe spend two years on a project, but she takes four. So she really takes such care with every single aspect, from the writing to the casting to the music to the editing. It's her sculpture. She certainly doesn't do anything like testing to see if an audience likes a different ending. She keeps her own counsel - trusts her own judgment - in an environment, at least in America, where that is happening less and less." While Allen has appeared in her share of blockbusters - The Bourne Supremacy, John Woo's Face/Off - she describes Yes as "a passion project". "I couldn't do them all like that because I wouldn't be able to send my daughter to college."

Yes is heavy on dialogue and low on action, which can make it feel more like a play than a film. You might even say that the rich language, not to mention the rhyming, at times make it seem as though it were written to be read rather than performed. "There's a place in cinema for that," Allen argues. "I wouldn't want to go to every movie where I had to work. But when I'm in the right mood ..." She says that Potter told her to think of the verse more in the spirit of Eminem than Shakespeare. When the director came out to New York, she took Allen to see Def Poetry Jam, a night of rap/poetry that ran on Broadway courtesy of hip-hop mogul Russell Simmons. Allen soon got comfortable with the notion of delivering a film mostly in iambic pentameter.

"Well, it made it really easy to remember the lines," she says. "And it felt very natural. Sally wrote it in such a way that you could do it more deliberately when the emotional moment was right - it would have a more apparent rhythm than at other times." The rhymes, says Allen, were for a reason. "When you are writing in that form, then it's almost easier to talk about larger ideas."

The film's larger ideas come to the fore in a scene in a car park where "He" tells "She" that they can no longer be lovers. "He" has just been fired following a racist incident at work, in which angry words with colleagues in the kitchen have turned from asylum-seeker-bashing to Islamaphobic verbal attacks. "He" pulls a knife on one of the chefs just as the boss walks in, and is shown the door. This experience sharpens his sense of alienation, and forces him to re-evaluate his affair with a married woman. Not only are they ethnically different, he argues, they belong to two irreconcilable, warring tribes - the west and Islam. "She" insists that she is an individual who cannot be held responsible for the actions of her government. "He" counters that these geopolitical inequalities are played out in their own relationship - while he speaks English and knows the Bible, she knows nothing of his religion and not a single word of Arabic.

Potter began writing the script on September 12 2001. "She knew there was going to be a great deal of negativity and hatred because of everything that had happened," says Allen. "She immediately felt, 'What is the antidote to that? Well, it's a love story of two people from different cultures.'" The nature of the material, says Allen, meant that conversation inevitably turned to politics during rehearsals. "We would watch the news together and things would crop up. Sometimes we would go through scenes and talk about the politics. We knew the most effective way to make the relationship believable was to make it intense and passionate. We hammered a lot of that out during rehearsal."

The burden "She" faces of being asked to answer for her nation's sins is not one that Allen has personally felt as an American. With the exception of a trip to Berlin, she says she has not been abroad that much to find out - but she doesn't sound the sort to take such criticism lightly if it ever came her way. "Over 50% of Americans don't agree with the administration: that's a lot of people. But they don't get the press." While she is no polemicist, Allen is definitely liberal; she lives among Democrats, and that comfort zone appears to be rarely breached. "I know myself and my friends in New York were devastated after the last election. We could hardly stand up it was so devastating. And those are the people that I'm around a fair amount."

Walk into a New York diner with Joan Allen and you do not experience that momentary silence when conversation and the clinking of cutlery halts to acknowledge the arrival of a star. Hovering contentedly between renown and celebrity, she is recognised for her work but has achieved relative anonymity outside it. "I'm hard to pin down," she acknowledges. "I tend to look different in films. I get recognised sometimes. But I just live my life. I get on the bus, I get on the subway, it's not a problem. I think of myself more as a character actor than that ingenue leading lady, who started out something like Michelle Pfeiffer, or Jessica Lange. I'm a bit quirkier than that."

She wasn't raised quirky. She was born and grew up in the small, conservative, midwestern town of Rochelle, Illinois, the youngest of four children in a working-class family; her mother was a homemaker and her father a garage attendant. She makes out that she stumbled across acting in search of adolescent romance. She had tried out for the cheerleading squad in high school, but when she didn't make it joined the drama society instead. "I think I knew acting was what I wanted to do," she says. "But I was from this small town and there was no place for an adult to recognise it. I think the cheerleading thing was a way of performing. There was the boy element, but more important was the performance element. Once I got to high school and auditioned for a play and got in, I thought this was really what I was looking for. Once that had got cleared up, from 13 on, that was it."

Boys would take more time. "That never really happened for me," she says. "I never liked the bar scene. I tried to like it. I would give it a try every three or four months. I'd think, tonight I'm going out. But I never met anybody in that circumstance."

At school Allen was something of a swot, graduating as the girl her peers thought "Most Likely to Succeed". "I was the good girl," she admits. "The straight A student, on the honour roll, part of the choir ... I played the cello badly. I did plays."

So what happened? First of all she got out of Rochelle and moved to Chicago. "How do we escape who we are?" she asks philosophically. "I think going to college, I felt freer. I loved the clean slate. I wasn't known as the sort of nerdy, studious girl. I met gay people for the first time in my life. I needed that expansion from a very conservative little town."

And then she met John Malkovich. "It changed my life," she says, without a hint of hyperbole. "I can't think what I would have done if I hadn't met him. I wasn't one of those kids who was like, 'Get me to New York. Get me to a big city.' I was always much more shy. All I knew was that I loved to act. But I don't know about the other part of it. I'm not sure I had the chutzpah to go and prove yourself."

With Malkovich's encouragement, she joined the Steppenwolf Theatre Company, which Allen describes as moving "into a theatre family". "We had our own theatre. We picked our own shows. I knew that I was doing plays one, three and five in the season. And we had a lot of security. We had a lot more security than most actors get to experience. Not financial security - the whole time I was with Steppenwolf I had a full-time job as a secretary - but the emotional security, to know that I could do what I really loved doing with an amazing group of people. Everything I've done since has been based on my experience with those people."

For much of her career she was typically cast not just as a wife, but as a film's ethical lodestar. "I think there's been a tendency to place me in what has been characterised as the 'moral centre' of the film. In films like The Ice Storm and The Crucible and Nixon, that's the sort of the persona that emerged." But somewhere around the new millennium, not long before her own 12-year marriage to actor Peter Friedman ended, she shifted gear - becoming more morally ambivalent as she moved from the periphery to the centre. In When The Sky Falls, a film about the life and death of Irish crime reporter Veronica Guerin, she's courageous but conflicted; in The Contender, as a senator running for high office, she's dogged by allegations of a murky past that could cost her the nomination, but sticks to her high principles regardless.

And, more recently, an array of entirely different personas have come to the fore. Two years ago, she played Arlene, an angry alcoholic widow in Off The Map. In The Upside Of Anger, which was released earlier this year, she was a sharp, suburban wife suddenly left to raise four wilful daughters on her own. And then, of course, there is Yes, where the moral centre lies in the plot rather than in the characters and where, as the unfaithful wife of a cheating husband, Allen is as compromised as everybody else. "That's one of the things I like about Sally's work," says Allen. "She doesn't deliver judgment on her characters. She doesn't say, this person's all good or this person's all bad. She shows them with all their flaws."

As we leave the diner, a man sitting in a booth by the cash register fixes his gaze on Allen, but he's the only person to have spotted her. Back outside her apartment, by the van and the food, I ask if it's strange to have this much effort dedicated to a few pictures. She nods and offers me chocolate mousse. And then she's up in the lift, heading for Nora and glamour.

· Yes is released on August 5.