Then an actress, her mother, Sharman MacDonald, was desperate to have a second child. But she and her husband, the actor Will Knightley, were young and broke. So he made her a deal: if she could sell a script, she could have a second child.

MacDonald wrote When I Was a Girl I Used to Scream and Shout, which was promptly bought by the Bush Theatre in London.

Within a year, she gave birth to Keira. “I’ve never worked for higher stakes,” recalls the Scottish playwright, as she gets up from a couch in the plush St Regis hotel in Los Angeles, where she is accompanying Keira to publicise her new film, Pirates of the Caribbean: The Curse of the Black Pearl.

If Keira hadn’t inherited the same remarkable talent for negotiating a deal, the young star’s image would not currently be plastered on the giant billboard opposite her LA hotel.

“I’m dyslexic, and when I was six my parents realised I couldn’t read and had been fooling everyone. The only way my mum could get me to work at my reading was if she promised to get me an agent. I didn’t even know what an agent did.”

So at the age of six, the precocious star got her agent, with the proviso that she would have to stop acting if her grades slipped. They didn’t, and after picking up 10 GCSEs and three A-levels from her London comprehensive, Knightley is now looking forward to getting on with her acting career.

Knightley was a relative unknown in America when she was in Los Angeles filming Disney’s swashbuckling Pirates of the Caribbean with Orlando Bloom and Johnny Depp earlier this year.

The film is penned by the same team as the animation blockbuster Shrek and produced by Jerry Bruckheimer, of Top Gun, Beverly Hills Cop and Pearl Harbor fame. In Pirates, Knightley plays a British governor’s daughter, Elizabeth Swann. Good pirate Jack Sparrow (Johnny Depp) and Swan’s sweetheart (played by Orlando Bloom) battle to save her from evil Captain Barbossa who is after her blood because he believes it will lift an ancient curse.

Judging by the buzz, it is the role that could transform Knightley into a global star. Her agent’s phone is ringing off the hook, magazines want her for photoshoots and critics in America are comparing her to a young Julia Roberts.

As her mother busies herself in the background, Knightley places her copy of Harry Potter and the Order of the Phoenix on a cluttered coffee table amid assorted research materials and make-up accessories.

The actress then slips off her shoes and folds her frame into the huge sofa and considers the ways this early flush of fame has affected her.

“It feels pretty much the same,” she says, “as I haven’t really been outside to see any of the posters. I was met at the airport by people with pictures of me for me to sign. Which is really a bit strange. A tiny bit exciting, and I think I’d be even more excited if I had not just got off an 11-hour flight and spilt coffee all over myself.”

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