The essence of female cool

And she was typically cool when she won an Oscar 10 days ago for Into the West, her anthem from Lord of the Rings. While the crowd in Los Angeles's Kodak Theatre cheered, Lennox quietly dedicated her performance to her mother Dorothy, who died last September aged 73.

"It was great fun to be sitting in the audience surrounded by the crew from Lord of the Rings as it won every category that came up," says Lennox, looking relaxed and fit in the drawing room of her £4.5 million Notting Hill town house, despite two-day-old jet-lag.

"But I thought that if I got caught up in the excitement of the whole thing I'd probably work myself into a frenzy and forget my words or trip over my dress or something," she smiles. "I thought, well, I've been through so much in my life I'm not going to let this affect me."

She has, indeed, been through a lot, but the death of her mother certainly caused her to take stock. It was, she admits, the first moment when she felt truly alone. "That was the predominant feeling - 'Oops, wow, now I'm on the front line.' Because I'm a single mother with two children, I have to be the strong one.

"It was great that my mother got to spend some time with us in her later years," she continues. "Because I'm an only child there are no aunts and uncles for the girls, no extended family, and I'm glad they got at least some exposure to that older generation."

Her daughters are, Lennox says, "the settled part of my life. I took a lot of time out from my career when I had my children. I realised that as a mother and a woman it was very important to get the balance right.

"I didn't want to stop my creative work, but I certainly couldn't go off on tour, or record an album every year as I used to. My kids have had the benefit of having me around and I have had the benefit of them." Now the girls are older - they are 14 and 12 - the situation is "more flexible" and she will soon start work on a new solo album.

Born on Christmas Day 1954 in Aberdeen, Annie grew up as the only child of boilermaker Tom Lennox and his wife Dorothy, a dinner lady; she says she always "lived a solitary existence", often creating imaginary friends.

The lonely, working-class girl won a scholarship to study the flute at the Royal Academy of Music but dropped out three days before her finals, explaining, "I wasn't gifted enough and I didn't identify with the people in that scene." In her early twenties she supported her singing ambitions with menial jobs.

SHE only achieved success with her sometime boyfriend Dave Stewart as the Eurythmics after their personal relationship - and their first band, The Tourists - had imploded. (She was recently estimated to have amassed a fortune of £30 million from the band and her solo career.) But coming to terms with her celebrity status proved a struggle and, despite her success, Annie always felt odd, different. "Maybe I'm just wired differently," she muses.

Her father allegedly disapproved of her brief 1984 marriage to a Hare Krishna monk called Rada Rahman, and in 1986 Tom Lennox died from cancer. Two years later, Annie gave birth to a stillborn son, Daniel, by her second husband, Israeli film-maker Uri Fruchtman. "We left the country," she later said. "You don't want people dipping their hands into your grief."

The couple subsequently had two daughters, Lola and Tali, but in 2000 their marriage collapsed, a painful event commemorated in the harrowing lyrics of her last album, Bare. "I certainly wouldn't advise divorce as a source of inspiration," she says drily.

She doesn't rule out another Eurythmics reunion ("as long as Dave and I are on the same planet there's always a chance") and her last collaboration with Stewart, a series of 1999 benefit concerts for Greenpeace and Amnesty International, seems to have stimulated her conscience.

"It is possible - without wishing to sound pretentious - to be an artist and contribute to the benefit of mankind," she says, "and I'm trying to work out how to do that in as intelligent a way as I can."

Still, though, her main hope for the future is her family. "As a mother, I would like to stay healthy and see my kids through their lives well," she says. "That's of primary importance for me."

What about romance, I ask? Annie Lennox looks at her watch. "Ah, just at this point I have to wind things up," she smiles. "How convenient ..." An attempt to reask the question generates a steely Aberdonian gaze and a firm " ... and that's my final answer."

I told you she was cool.

The album Bare is out now on BMG records.