Child actors, bless their precocious and faintly terrifying little hearts, have a less than astonishing record across the entertainment industry. If they don’t end up locked in a Manhattan apartment, engaging in costly legal battles with their parents, they’re likely to be driving a milk float in a “Where are they now?” feature. There are exceptions - Elizabeth Taylor, Hayley Mills and Roddy McDowall spring to mind - but they are rare. This year, however, Jemima Rooper stands on the threshold of joining them; and, almost uniquely, she looks set to do so as a serious actress rather than a cutesy ditz.

Rooper carved out a career for herself from an early age. Her mother, the Radio 4 newsreader Alison Rooper, flatly nixed the eight-year-old Jemima’s request to join the second oldest profession, so her daughter went through the phone book, calling agents herself. She even attended an open audition for Oliver! dressed as a boy.

“I think what triggered it was watching films like Annie and thinking, ‘I want to be one of those kids’,” she explains, now 26 and huddled in a thin T-shirt and leggings against the howling July wind on the terrace of the National Theatre, where she is preparing to make her debut in Her Naked Skin.

Her determination secured roles in a series of children’s television dramas, from George in The Famous Five, in the mid-1990s, to Bobbie in The Railway Children. Her school, however, insisted that she stick to her studies, which meant “while doing a 10-hour day at 14, I was having to do exams at one in the morning”. She pauses, adding wryly: “And that took its toll a bit.”

The early Noughties saw her enter the world of sci-fi, with roles in the teen shows As If and Hex. She picked up a hefty sci-fi following, which resulted in a brief flurry of activity from Doctor Who fans lobbying for her to get Catherine Tate’s job. Her Naked Skin is a switch - it’s a period piece about suffragettes imprisoned in Holloway - but it has something in common with her sci-fi career. “It’s my fourth lesbian,” she giggles. There was Hex, a cameo in Sugar Rush, as a lesbian rock star, then The Black Dahlia.

“My Naked Skin character, Eve, meets Lady Celia Cain [she adopts a melodramatic tone] over peeling potatoes. Eve basically falls head over heels in love. When I read the script, it touched something - the love story is intense and powerful, so maybe it’s something to do with the way I like to love people. In my personal relationships, I’m full-on and like to be completely wrapped up in it.”

Her Naked Skin is a new play by Rebecca Lenkiewicz - “The first play by a woman in the Olivier,” Rooper declares proudly - and it’s proved something of an education. “I remember touching on Emmeline Pankhurst when I was 11 or 12, being told women didn’t always have the vote,” she says. Her reading exposed her to the “Cat and Mouse Act”: hunger-striking women were not force-fed, but were allowed to become weak, released and rearrested when they were healthy again. “I’ve always been a feminist, but without the real knowledge of where it all came from,” she explains.

Her next role - and one that could be her breakthrough into living rooms across the land - is in ITV1’s primetime autumn spectacular Lost in Austen. Rooper plays a modern woman who steps into the plot of Pride and Prejudice. It gives her a chance to display a fine range, from serious to slap-stick: “I turn up at balls and don’t know the steps, but I’m pretty outspoken, so slowly start to influence other women and change the plot of the novel.”

This all sounds a bit earnest until she gets onto her latest hobby - burlesque and pole-dancing. “Burlesque is hilarious,” she says. “It’s like being at school when you’re eight, and you go, ‘Let’s make up a dance.’ It was supposed to make us fit, but it just made us giggle a lot and drink wine, so we did a pole-dancing class as well. I now have a pole in my living room. I hate the gym, so the idea is I spin around it and get fit that way, but it hasn’t worked. Boys ruined it for me - every time they spin around it, they have much better upper-body strength, so they can do amazing tricks.”

At the moment, Rooper is single, which gives her the freedom to head off to LA this autumn to see what’s going on. “I don’t know if I could really live in Hollywood - I’m too wonky,” she says, looking every inch a perfect, pretty young woman.

“I’m never going to be Sienna Miller or Keira Knightley, because I don’t look like them. My flatmate’s girlfriend is 23 and gorgeous, and she’s friends with Keira Knightley. We all went out and I was looking at them thinking, ‘Yeah, that’s why I play my roles and you get big movies. I get it now. I look weird.’”

She shrugs. “I like the fact that I play edgy characters - for someone in my twenties, where you do get stereotyped roles, I’ve had parts that aren’t the norm.” She starts heading back to rehearsals and her Victorian lesbian seamstress locked in Holloway prison, then turns to make things absolutely clear: “And, frankly, I want that to carry on.”

Her Naked Skin previews at the National Theatre, SE1, from July 24. Lost in Austen is on ITV1 in September

Editor's choice

• Are Glasvegas the new Oasis?
• Proms Podcast with Stephen Hough
• Vote for musical perfection