"I put self tanner on, since everyone does in L.A.," says the actress, unfamiliar with the patience required to sit still while the lotion soaks in. She pivots her peppermint-striped legs, tanner streaking around her pale skin in finger strokes. "Isn't it terrible?"

Not that Williams has much to complain about these days. Last January, while she sat in her London flat eating beans and rice and lamenting her status as an out-of-work actress, Costner was pacing his L.A. production office in a panic. Two weeks away from a start date on The Postman, he still hadn't found the right person to play Abby, an independent woman in a postapocalyptic society, looking for a man to inseminate her. Costner "was at serious wit's end," says producer Jim Wilson. "We had gone through several gals, there just wasn't the right chemistry."

In desperation, a call went out around the world. Williams, whose only on-camera performance had been a British TV adaptation of Emma, was invited to audition on video. She didn't think she had much of a chance. "When your agent says you're going on tape for Kevin Costner, it's a bit of a joke," says the actress, who is the daughter of two barristers and the younger sister of a London lawyer. "I thought, I'm not wasting money on a taxi for this, I'm going to cycle. It was raining, so I had mud on my face, and [when I got there], the secretary in the office is reading Kevin Costner's lines, and I did a terrible Southern accent. Because the situation was very funny, I was laughing quite a bit."

Costner, who directed the film and stars as its loner hero, says it was Williams' smile that got him. Twenty-four hours after she got his nod, Williams was flying to L.A. for a live audition and ensconced for the first time in first class. Somewhere over the Atlantic, however, she discovered that her Postman script included only every other page of dialogue.

That evening, spinning with jet lag and nerves, she had dinner with Costner at her hotel. "There was that thing, You're Kevin Costner, across the table," she says, "and you have to make sure you don't stare. You mustn't stare. Okay, look at the food." The following morning, Williams auditioned with Costner for the producers, returned to her hotel room, and received a call: The part was hers, would she work on her American accent, and could she be fitted for her wardrobe in an hour? "It was," Williams says, "as if I'd been kidnapped by aliens."

The kidnappers had their own concerns as Williams headed to the Postman set in Metaline Falls, Wash. (pop. 225). "She could have gone out and cracked up," says Wilson. "She could have been a nutso. It was a huge gamble." Admits Costner, "I was never sure she was right until the first time I saw her on film."

Williams ended up being quite sane, if unwilling to play by the help-me-I'm-a-star rules. As a woman who admits, "I hate prissy handicrafts and sh-- like that," she insisted on doing a stunt in which she lands in 38-degree water ("Try that with an $8 million actress," says Wilson). "My face had this extraordinary color," Williams says. "Jim actually said to the makeup woman, 'She has too much blue on her cheeks.' The woman said, 'That's not makeup. That's what happens to an actress when you drop her in cold water and leave her there for seven takes.'"