Leeves arrives at the photo shoot dressed in a Gap T-shirt and jeans, with wet hair scraped back and no make-up. But within minutes she's surrounded by personal make-up artists and hairdressers, and a publicist fussing around checking the room temperature. It makes you realise how far she has come from her East Grinstead roots and first job on television - running about in a bra and pants on The Benny Hill Show.

Perhaps this has prevented her from turning into your usual spoilt Hollywood horror. There are no limos or bodyguards on display. "When I go to the supermarket, people often recognise me and follow me around," she laughs. "Sometimes they approach me and say that they enjoy the show, which I like. They're often surprised to see me doing the shopping myself, but I don't have a PA like everyone else over here. In fact, I only have a housekeeper, who comes twice a week." She describes her off-screen personality as a "housewife who works part time on a television show", although she is now Hollywood enough to share a stylist with Kim Basinger and Cate Blanchett.

One of four children - her sister Kayte now also lives in LA and acts as her manager - Leeves was brought up in West Sussex. "I had a normal childhood, but from the age of five was desperate to embark on a theatrical career. My parents saw how serious I was and decided that I should go to drama school."

After school, Leeves did the usual rounds of auditions until, in 1980, the 18-year-old landed an audition with Benny Hill. "It was bizarre, as I had to go to his house, which had been furnished for him by the TV Times - and it showed. I had to go through a number of sketches with this lonely, unhappy man. Having said that, he was encouraging and told me that I had talent." Her appearance as a Hill's Angel didn't quite ignite her career, however. So, after a sketch on Morecambe and Wise, and a part as an uncredited extra singing Every Sperm is Sacred in Monty Python's The Meaning of Life, Leeves decided to swap Benny Hill for Beverly Hills.

"I arrived in LA with $1,000 and the address of a man I had met in Paris and hardly knew. He had told me I was welcome to stay with him any time, and I had taken him at his word. I was very young, and that was the beauty of it - I had nothing to lose. Even so, I was completely broke and it took me a year and a half of grinding poverty before I got my first job."

In the meantime, she took acting classes - fellow students included Jim Carrey, Ellen DeGeneres and Winona Ryder - where she would offer to clean up after rehearsals if food had been involved. The leftovers were practically all she got to eat. To earn the tuition fees, she appeared as a dancer in rock videos, put herself up as a babysitter, sold souvenirs and packed fingernail decorations in a factory (until she was fired for chatting).

It was a period of black depression, and she has said before that she had two nervous breakdowns. "I had nothing to eat, no money and I simply couldn't stop crying. I kept asking myself, 'What am I doing here? What have I done?' " Finally, after a couple of small roles, she got a guest spot on Seinfeld, playing the sex-starved virgin Marla. This obviously got her noticed: shortly afterwards, when she was sitting in a doctor's waiting room, a man seated opposite her suddenly shouted: "You're the virgin! You're the virgin!" And then along came the audition for Frasier. The on-screen chemistry between her and its star, Kelsey Grammer, was such that she was hired on the spot.

As for the accent, that was apparently her idea. The producers wanted the character to sound distinctively working-class British, but knew that the American audience wouldn't understand a "mockney" accent. Neither would a genuine Northern burr go down any better - The Full Monty had to be subtitled for its American release. So Leeves, whose real accent is home counties with a hint of LA, came up with the fake Lancashire lilt.

The actress now earns more than £64,000 per episode and, apart from Tracey Ullman, is probably the most popular Brit on American television. Her love life has also, after a few false starts, come together. Back in 1994, she joked on a chat show that she hadn't had a man in her life for four years, but this all changed a year later when she met Marshall Coben, a vice-president at Paramount. He's good-looking in that white-teeth, all-American way, and Leeves says it was love at first sight. They married in her back garden 12 months later.

As for developments of that nature on air, she lets slip that romance could finally be on the cards for Daphne and Niles, too. And, as Leeves is keen to start a real family, we could be in for some other interesting twists in the plot. There are certainly no plans to leave the show, however. All too predictably, Leeves gushes that the cast are her best friends off as well as on set. "Frasier has been such a magical experience for everyone involved that no one wants to leave," she says. Although she admits she'll never forgive Moose - the show's dog, Eddie - for making it onto the cover of Entertainment Weekly before her.

Leeves has dabbled in other projects with varying degrees of success. She was the voice of the Lady Bug in James and the Giant Peach, and starred alongside Meryl Streep in last year's Music of the Heart. But what excites her most is that she and Peri Gilpin - who plays Frasier's sidekick, Roz - have formed a production company called Bristol Cities. Her LA friends haven't yet got the joke. They may have caught on to mid-Atlantic Mancunian, but cockney rhyming slang is another matter altogether.

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