Claire Skinner: From washing up to the West End

The other day Claire Skinner was watching a documentary about a schoolgirl from the Isle of Man when she felt a flash of recognition.

"She was dancing in her bedroom doing this mad kind of Japanese dance," says the silver-voiced star of Outnumbered. "She had become a real hit: this ordinary girl doing something quite extraordinary. And that tickled me. It felt quite like me."

Skinner may be 45 and, thanks to her role as a beleaguered mum in the BBC's improvised family sitcom, now recognised in the street, but part of her remains an ordinary girl from Hemel Hempstead. In a south London rehearsal room she is twitchy and nervy and still betrays traces of the girlish shyness that crippled her as a child. Yet there are also flashes of the steely luminosity that has caught the eye of directors from Alan Ayckbourn to Mike Leigh. Skinner is an actress whose name might slip past you, but whose performances you rarely forget.

She is about to star opposite Simon Russell Beale in Matthew Warchus's revival of Ira Levin's 1978 thriller Deathtrap. The trailer for the show has already received numerous hits on YouTube, and the play itself, about a creatively moribund playwright who murders a budding young writer and steals his new script, has been rewritten in order to introduce new twists – and is strictly under wraps. It's the kind of slick, populist West End comedy that Warchus – who directed Boeing Boeing and recently La Bête – excels at, and it's also about the last place you'd expect to find Skinner, who on stage at least specialises in damaged, flinty women. But that's partly why she's doing it. "I did Mrs Affleck last year at the National," she says, referring to Samuel Adamson's reworking of Ibsen's desolate domestic tragedy Little Eyolf, in which she played a woman consumed by guilt and obsessive love for her husband. "It was very dark; it quite took it out of me. So I wanted to do something fun, something lighter. Although it can be a bit awkward and painful in the rehearsal room. My character doesn't have many lines: there are all these gaps in her and I've got to try and fill them. So I'm the one going, 'Hang on, I just don't know how to get over this little bridge here'." She trails off. You half expect her to start chewing her fingernails.

A vein of nervous worry seems to bubble away beneath the surface of Skinner – it's as though she carries an imaginary string of rosary beads around with her. She is small-boned, fresh-faced, has the sweet voice of a child, and appears constantly unsure of herself, glancing round the room like a bird. Yet she's not bothered by this: she thinks most actors are consumed with anxiety. "There's that terrible 'look at me, don't look at me' thing that goes on, isn't there," she says disarmingly. "Actors do such a good job at pretending they are all right. That's what all the 'darling' and the 'luvvie' is all about, whereas actually they are all quite paranoid. Well not all of them. Perhaps I'm speaking for myself."

Skinner – who already had a respectable TV career under her belt with Life Begins and more recently Sense and Sensibility and Lark Rise to Candleford – is now a bonafide star, thanks to the surprise, slow-burn success of Outnumbered. The show's great conceit was that Skinner and her on-screen husband, Hugh Dennis, both had a script, but their three children – played by Tyger Drew-Honey, Daniel Roche and Ramona Marquez – did not, meaning that Dennis and Skinner were continually led by whatever the children said. "It was terrifying to begin with," she admits. "Hugh and I said: 'we're just going to have to trust Andy and Guy [the writers Andy Hamilton and Guy Jenkin], aren't we?' But doing it has made me more confident as an actress. It's helped me to trust my instincts, which I've never really done before. Usually I go back and back with a character, building up a back story. Whereas with Outnumbered, it's about going with the first thing that comes to you, because of what the children are saying. Which of course is what parents do all the time."

Skinner is no stranger to improvisation – she broke through with her work in the early 1990s with Mike Leigh. She created the role of Natalie, the inscrutable snooker-playing sister to Jane Horrocks's neurotic, stringy, chain-smoking Nicola in Life Is Sweet, and the prissy, house-proud Sandra opposite David Thewlis in Naked, although she points out that Leigh improvises in an entirely different way because there was ultimately always a pretty rigid script. Yet for many it's her stage work that really stands out – her emotionally manipulative, cruelly unmaternal Mrs Affleck; a spirited, heartbreaking Desdemona in Sam Mendes's 1997 production of Othello for the National (Russell Beale played Iago); and an outstandingly fragile Laura in the Donmar's 1995 production of The Glass Menagerie (also directed by Mendes). She's played Isabella in Measure for Measure and Hermione in The Winter's Tale, and each time, she says, the challenge has been to find the iron behind the porcelain, or as she puts it, "a character that looks like one thing, but who beneath the surface has some barbs in her."

Desdemona drove me nuts!" she says. "I'd go, 'No, I've found the strength in her', blah blah, and yes, you do for a bit, but after a while you think: well, you haven't given her strong lines, you've given her weak lines, and even when she is fighting for her life she's got a weak line. I seem to have spent a lot of my time as an actress trying to find the ways in which these characters are not weak – and that's valid and creative and good. But that's why with Mrs Affleck, who is very aggressive and very much on the front foot, I felt really free. In a funny way, she was the inside out of me."

She admits she has spent most of her career fighting other people's perceptions of herself. "I think it's partly the vocal quality, isn't it?" (She has this delightful unforced way of talking that suggests she has only just thought of whatever it is she is saying.) "People go, 'Oh well she's slightly built, she has this voice' – and it drives me mad that strong women are meant to have deep voices. I do look at other actresses sometimes and think: 'People take you slightly more seriously than they do me'."

She grew up as the third child of a shopkeeper and an Irish-born mother and realised at school that the theatre was where she belonged. "I was quite an introverted child and I found it hard to find my place," she says. "I felt dislocated and disjointed, with this interior world going on that no one could access. But then I had this wonderful teacher who made this wonderful, inviting space in the drama studio." At LAMDA, however, she didn't fully blossom. "I hesitate to say I had a sheltered upbringing, but it was Brownies and Guides and the Catholic Church and I was fairly young and unformed, a naive 19-year-old," she says. "I didn't feel properly awake until I got out." But then she went to Scarborough to work with Alan Ayckbourn, often finding herself playing characters 20 years older than herself, but nonetheless having the time of her life. "Ayckbourn's plays are amazing. I honestly think it's time for a major season of his work. Those were great years. I also did Othello there too [she played Desdemona again]. Opposite Michael Gambon. Who blacked up. Amazing, isn't it."

She now lives in north London with her husband, Charles Palmer, the son of actor Geoffrey Palmer, and their two small boys. "It's weird – people often come up to me and ask about the Outnumbered children in front of them. My husband grew up with a father who was a national icon and it was there all the time, so we're quite aware, quite careful. I needed and wanted to have children, but I thought acting might fade away a bit, that the desire would go," she adds. "But it hasn't. So they both need to happen."

'Deathtrap', Noel Coward Theatre, London WC2 (www.noel-coward-theatre.com) to 22 January