Davis’s portrayals of neurotic thirtysomething women with calamitous love-lives have earned her the nickname “the arthouse Ally McBeal”, but in The Matador she plays against type and is, for once, neither clumsy nor plain. She also stars as Nic Cage’s estranged wife in another film released this week, The Weather Man.

In Matador Davis’s character, Bean, is a beautiful, ingenuous wisp of a housewife who becomes enchanted by Pierce Brosnan’s misogynistic hitman. “Have you seen the movie yet?” she asks urgently. “Did you go to a private screening? Wasn’t that weird, watching the film all by yourself? I saw About Schmidt (in which she starred alongside Jack Nicholson) by myself and worried that nobody would like it or get it, and it wasn’t until I saw it again and saw the audience reaction to it that I and realised that it worked. So I stopped going alone.”

Working with Brosnan was “amazing, but not glamorous”, she says. “Nearly all of The Matador was shot in Mexico City. I was ten weeks pregnant and Mexico City is the last place you want to be when you’re pregnant.

“I was soooo sick. We had a bucket on the set and Pierce made sure it was always near by. I also had two bodyguards around the clock, which was strange. Our wardrobe guy was actually kidnapped and taken around different cash machines and then sent back.”

She claims that the acting career just sort of happened; things simply fell into place. “It probably helps,” she says, “that I’m not the beauty queen type. I’m happy to look plain on-screen, which makes life easier. It’s hard work looking perfect.”

She admits to being “peeved”, though, when she was offered a role opposite Johnny Depp — as his mother. “We’re exactly the same age (not so, actually — he’s 42, she’s 41). That tells you something about the absurdity of this industry and the whole age thing. Of course I turned the role down.”

She didn’t grow up dreaming of becoming an actress. As a teenager at school in New Jersey she signed up for drama classes to help her overcome her shyness. Soon, though, she was writing and staging plays with her then neighbour, the actress Mira Sorvino. But acting was not a career option. “There were no actors in my family. Tenafly, New Jersey, wasn’t exactly a hotbed of artistic talent,” she says. “My dad worked as a salesman and was a bit of a drifter and it was left to my mother to raise and send us three children to university.”

Davis studied science at Vassar University. Even so she came back to acting, studying at the Royal Academy of Dramatic Art in London. Returning to America, her first role was on the stage, stepping into Madonna’s shoes in the Broadway production of David Mamet’s Speed-the-Plow.

“I still had no great ambition,” says Davis. “I auditioned for what seemed like millions of movie roles and never got anything.”

Eventually she broke through; her first role was in the thriller Flatliners (1990), playing William Baldwin’s girlfriend. “Now,” she says, “I’m aiming for longevity.”

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