Hotel playwright Polly Stenham: 'It's a good experience to get bad reviews'

"It feels a bit like playing for England, or something," says Polly Stenham, gazing out of a window on the fifth floor of the National Theatre. Not that Stenham, 27, is daunted by the prospect of making her debut on the South Bank with her fourth play, Hotel. This is a playwright who wrote her first play when she was 19 years old. That Face premiered at the Royal Court when she was 20, was hailed as "one of the most astonishing debuts in 30 years", won all the awards, transferred to the West End when she was 21, and to New York when she was 23.

So, no, she's not nervous. "It feels comforting. I've come here since I was a kid. There's something about the foyer and how big it is, and how much of an institution it is, that feels really safe," she shrugs. There's a bit of the rebel about Stenham, in her black skinny jeans and biker jacket, with her punkish blonde hair, chipped black nails and silver ring in the shape of a lion, her boarding-school vowels dampened by a touch of estuary.

It might all come across as a bit too-cool-for-school if she wasn't also so clearly thrilled to be here, doing what she has wanted to do, "from a preposterously, pretentiously young age". She is childishly excited to have her own pass that lets her wander from backstage to front of house. "SO. MUCH. FUN. I cannot get over being able to do that. When you're in the bowels and it's all quiet and then you slip out of what looks like a fake door and you're suddenly outside and it's all carpets and Maltesers and people in nice glasses..."

It is precisely these cultured, middle-class types, with their Maltesers and nice glasses, that Stenham has set out to discomfort ever since her dazzling debut about a dysfunctional, well-to-do family of boarding school brats and their alcoholic mother and absent father. It was hailed as a breakthrough for the Royal Court – finally daring to put the people in its stalls on the stage. "It's good to rub people's noses in it. That movement really needed to happen. I mean, it was getting pornographic. Here I go in my pearls to watch some skagheads…" Theatre should shake people up. Take the recent string of flop musicals in the West End. "It serves them right," says Stenham. "There's a patronising element, that people expect them to want the same old shit."

Hotel is a revenge thriller set on a luxury island resort – a paradise family holiday turned to hell. It was inspired by a recent trip to St Lucia, where Stenham has been holidaying since she was 14 years old. "I was on holiday and I had this really dark thought…" she sniggers. "I suddenly realised there was something kind of absurd about where we were. You holiday in these incredibly beautiful places but they're very poor and sometimes very dangerous. The post-colonial arrogance of it is amazing. It's a stage set, you know? Fabulously rich dramatically."

It is a departure for Stenham. That Face and its follow-ups Tusk Tusk, about a family of children left home alone, and No Quarter, about a young man who carries on living in the crumbling family manor after his mother dies – all dealt, broadly, with unstable children trying to undo the damage done by disastrous parents. She would like to publish them as a trilogy. "Called 'Milk'". Like mother's milk? "Yeah. I'd call them a portrait, really."

It has always been tempting to map Stenham's life story on to her plays. She went to boarding schools, Wycombe Abbey, then Rugby, and her parents divorced when she was 14. Her mother, Anne O'Rawe, a painter and an alcoholic, moved back to Ireland and Stenham was brought up by her father, Cob, a colourful businessman who had a Porsche as his company car at Unilever and was chairman of the Royal College of Art and the ICA. He introduced his daughter to the theatre and writers like Tennessee Williams and Edward Albee who would become her favourites. He died of a heart attack in 2006, the day after That Face was picked up by the Royal Court. It is dedicated "To Cob, who's watching from the gods."

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In 2012, her mother died from cancer, making Stenham an orphan at 26. She was writing No Quarter at the time. In it the lead character helps his mother, a dementia patient, to die, before partying his own way to oblivion. "It was more like a kind of scream," she says. "I spent a lot of time on him, he was quite a haunting character… He felt like a kind of weird, dark, twin brother." She wasn't really surprised when not everyone liked it. "You know when it's good and you know when it isn't. I loved it the most, like the way you love the most difficult child, maybe? Because it was deliberately not a crowd-pleaser." Now she lives in the family home that she inherited, a Highgate mansion with Warhols on the walls, with her younger sister, Daisy, and a substitute family of friends. "Finishing that trilogy felt really good. That feels like my early work. And it feels done."

No Quarter took her four years and 18 drafts ("Too many"), Hotel took eight months. "A bit like a bullet. BOOF." Is it easier to write now? "It's funny, the more you do, the better you get technically but the harder it gets to block out the bullshit. It can be very corrupting all that stuff." When That Face was first on, she would hang around the bar and ask people what they thought, because nobody knew who she was. Now audiences watch her instead of her play. "At No Quarter people would come up and say, 'You were mouthing the words.' Creepy much? That's a bit rubbish about having more of a profile. I liked feeling a bit more anonymous."

She read all of her reviews for her first play, "Because they were all great!" but is more choice these days. "My last one the reviews were insanely mixed – very good or very bad and that was a good experience." She is sanguine too about That Face's New York flop. "I always thought it was a play the whole world would like but actually it turns out it's really British," she says. "It was a really bad production. But it's too dark and they did NOT find it funny. And if you don't find it funny it's just this howling melodrama. Because I was so blessed – blessed, urgh – with good reviews for both my first plays, it was really good to actually go off-shore and fail."

She always loved writing and the theatre, but it took her a while to link the two. After school she worked as stage manager at Bromley Theatre and the Arcola and then studied English at UCL. When she was 19 she joined the Royal Court's Young Writers' Programme – "because I couldn't find a course for writing a novel" – and the penny dropped. Now she works most days in a studio at the Cob Gallery in Camden, which she co-owns with her sister and friend Victoria Williams. "I have my big blackboard and I try to treat it as much like a craft, not like an art, as possible. Hands dirty."

The success of That Face was "dreamlike. Brilliant but disorientating, for a little while." There was a bit of high-profile partying, with her friends Matt Smith (star of That Face), Florence Welch and her one-time boyfriend Harry Treadaway. These days she is dating the artist Eloise Fornieles, and feels more grounded. "I no longer feel anxious about this being my career. I know it's my career," she says. "It feels less like a weird act of God. I don't have to prove that it's not a fluke anymore. That's really nice, to have relaxed slightly. I love doing this. I'm good at this. Now I feel like it's the beginning of a longer journey."

She is already looking beyond the theatre. She has written a screenplay of Tusk Tusk to be directed by Clio Barnard (The Selfish Giant). Foxtrot, her kitschy kidnap drama set in Soho and starring Billie Piper as a stripper and Lindsay Duncan as a madam/ gang boss, screened on Sky Arts last week. It was her first time directing. "Oh I LOVED it," she hugs herself. "My girlfriend said afterwards, 'Literally, it took you a week to come down from that.' Yes, a bit of a power trip but I just loved the get up and go of it."

She is now working with Nicolas Winding Refn, director of Drive on his new film I Walk with the Dead. "He wanted to write something quite girl-strong because most of his stuff isn't." When Stenham emerged she was fêted as one of a wave of young, female playwrights, with Lucy Prebble, Laura Wade and Anya Reiss. "Such a strong contingent of girls. But I don't think anyone's writing is particularly female. It's a minefield, that." Is she a feminist? "I'm feminist in the sense that I believe in equality. Completely. I've been very, very lucky, because I've always probably been treated better for being a girl… You do encounter the odd discrimination, like being asked if you're the work experience girl at the Faber party. But if I was a 22-year old boy, they'd probably say the same." The protagonists of her last three plays have been male; the next will be too. "I do feel that potentially I should be writing more roles for women. In Hotel the women carry the heavy, violent politics – that was a conscious decision." Next year she will reunite with Jeremy Herrin, director of her last three plays, for a new take on Antigone at the Donmar. "Maybe I'm redressing the balance. But I do like writing boys, weirdly. Maybe it filters me more.. But then, write what you want to write."

It's what she did with That Face, after all. "It's funny. I very nearly just didn't do it. It does always make me think, 'Well, why not just try windsurfing?' It is so important to just give shit a shot. You never know, it might be the thing that changes your entire life."

'Hotel', National Theatre, London SE1 (020 7452 3000) to 2 August