Dr Who star travels back in time to play Sixties model Jean Shrimpton

Gillan, 23, who is also a former model, plays Shrimpton in BBC Four's We'll Take Manhattan, which explores the model's relationship with photographer David Bailey.

The film, due to be shown in January, focuses on a week in 1962 in New York when the British pair, who later became lovers, first met on a photoshoot.

Gillan, who finishes her first professional stage appearance in Inadmissible Evidence at the Donmar this weekend, had not been able to meet her subject before making the film.

Shrimpton, 69, withdrew from the spotlight more than 30 years ago and runs a hotel in Cornwall. But Gillan said: "She left a lovely message saying she really enjoyed it. David Bailey loved it too. And they're really honest people so that means something to me."

Gillan added: "I find her really, really intriguing." She enjoyed recreating Bailey's shots that epitomised Swinging Sixties style. "I got to wear the most beautiful replicas of the clothes for a shoot in Vogue."

Aneurin Barnard, 24, who last year won an Olivier Award for his role in Spring Awakening, plays Bailey.

Gillan, who was a guest presenter at the Evening Standard Theatre Awards on Sunday, said she had loved making her professional stage debut.

"It really opened my eyes to so many things. It's good experience to get an instant response, the buzz, adrenaline. There's nothing like that feeling. It's a really scary thing to do."

But she could not imagine any job being more enjoyable than Doctor Who, to which she returns next year: "It's been so amazing. I don't think I will ever have a job quite so fun ever again."