Polly's dramatic debut

She prefers not to talk about her mother, who hasn't had much involvement in her life "since I was 13". It was Cob who took Polly to see Pinter, aged 11. Later they hunted out the most avant-garde fringe plays together. "It was our thing. He introduced me to Sarah Kane and Shunt. We must have cut a very odd pair at these things: he was very old and I was very young. But I really owe my love of theatre to him." Daisy also acts and is a member of the National Youth Theatre.

We meet at the Royal Court café. With her urchin haircut and delicate features, Stenham is lovely to look at. Dressed in jeans and a Fred Perry-style shirt, she radiates both feminine and masculine energy. You'd expect someone who writes so penetratingly about family misery to be a bit dour but she has a real sense of fun. In fact, Stenham has hit the headlines before. In 2005 a newspaper gossip column reported she had married her "lesbian best friend", Jeff Banks's daughter, India, whom she had met at Rugby school. When the story broke, the two 19-year-old girls were travelling around the world on a gap year, and Banks was quoted as saying he had met Polly ("a wonderful girl, very special") and welcomed the relationship. Since then whole websites have been devoted to the topic.

Stenham is very straightforward when I approach the subject - with some trepidation. "This haunts me. I think the best thing is to be completely honest. I did have a relationship with a girl, yes. But now I have a relationship with a boy. So both things can happen to anyone. But I did not get married, they didn't even check their facts, it was hysterical. For a start it wasn't even legal to marry at the time. Could you also stress I have a boyfriend now," she pleads. "I really do not want to come across as a lesbian." For the record, he is an actor, whom she has met since That Face.

The production brought Lindsay Duncan back to the theatre for the first time in five years. So often cast as the English rose, she played the alcoholic mother, Martha. "Seeing her in her bedroom in her nightdress, pissed, the veneer goes, doesn't it?" Stenham grins. "But hopefully some rougher charm comes through. I made an effort to write Martha as charismatic because I didn't think she'd get away with being so cruel unless she had a degree of allure." There were also plum roles for Felicity Jones and Matt Smith (who is also nominated for the Standard's Milton Shulman Award for Outstanding Newcomer).

The play opens with two girls tormenting a younger girl who has been tied to a chair, a beanie hat obscuring her face. Moments later, she collapses, having had her drink spiked with Valium. Stenham wanted to show that young women are not angels. "Give me a 14-year-old girl who's angry! That's an age and a species of the human race that can do some bad things. There are hormones everywhere."

Stenham was a boarder at Wycombe Abbey, Buckinghamshire, then moved to Rugby for the sixth form. She is very careful - no doubt for legal reasons - to talk generally about a culture of bullying in both boys' and girls' boarding schools. Nothing like that happened to her, she insists, she was in a very nice house with older girls.

But, I say, a contemporary who was at school with her at Wycombe remembers a terrifying initiation rite called Corruption, where new girls were made to undergo humiliating rituals, such as running naked through the house or cleaning the lavatory with their toothbrush. "These things go on," Stenham agrees, "not to that extent, this is a heightened version, but things of a degree did go on at that school, and I'm sure at all kinds of schools. The authorities did make a real effort to stop it. But the thing that got me thinking about it was Guantanamo, and those pictures of the prisoner with the hood, and another on a dog lead. I thought 'Oh, my God'," she says in recognition. "It got me thinking how boarding school is much like the army. As Mia says in the play, it seems all right until the minute you step out of it, as I'm sure the torture in those jails - in context - seemed OK."

Stenham is a graduate of the Royal Court's Young Writers' Programme, along with new stars Mike Bartlett and Lucy Caldwell (whose play Leaves is also up for the Charles Wintour Award for Most Promising Playwright). After taking A-levels, she worked as a backstage "skivvy" for the Ambassador theatre group and as a "god-awful stage hand at the Arcola in Dalston, near where I used to live". She started researching writing courses and applied to the Court's 10-week programme.

"It's just brilliant, I can't speak highly enough of it. It's not elitist; it's open to anyone aged 13-25. You just go in and read plays and write little scenes. I really believe that with that behind you, anyone could have a good shot at doing something like this," she says, gesturing at the famous posters on the walls of the Court. "They said write a play, if you want, for The Young Writers' Festival, and I thought I'd give it a go." The result was That Face.

She still lives in a flatshare with a group of students in Highgate. No, she says, they don't envy her success. "They're all doing these very hard, serious degrees. They're bright people." In the early stages, they helped her battle with the structure of the play (in the programme she gives thanks to "Team Deathbat"), acting out the parts in their sitting room.

As for having a father who was so much older: "It's given me a strange rapport and real adoration for men of that generation. I'm very comfortable sitting for hours chatting to men in their sixties. They're so well-mannered. They listen, which I find slightly lacking in the generation just below me."

That Face won comparisons with Noël Coward's The Vortex (also a mother/son triangle). In fact she'd never even read the play until this year. Her heroes are "old-school" playwrights such as Pinter and Caryl Churchill, although her own style tends more to the American writers Edward Albee and Tennessee Williams. "The blood and the guts of it, the slow burn; the way each character is very built from the feet up, it's almost a more novelistic way of writing plays." And she loves Sarah Kane.

She is writing her second commission for the Court, which will be re-staging That Face in the main theatre next summer. Despite royalties and her inheritance from Cob, she still lives and dresses like a student. Her guilty pleasure is watching The Royle Family back to back with Friends. "You should try it, for the contrast," she recommends. And she might go back to university. "I think I'm not done with learning. It's good to have chewy things. The way I look at it is, this is all a happy accident. I just love to write."

The £25,000 Charles Wintour Award for Most Promising Playwright is jointly donated by Lord Rothermere, the Evening Standard's proprietor, and American Vogue editor Anna Wintour, in honour of her father, Charles Wintour, a former Evening Standard editor and founder of the awards. See later editions of Tuesday's paper for a full list of winners of the Evening Standard 2007 Theatre Awards.