Are you about to fall in love with this woman?

She wasn't due in London for a week. In fact, she was supposed to be in Florence. But you can't miss the birth of your own baby. So, at the capital's newest elite fashion store, no one was too surprised on Thursday afternoon to see an emotional, intense, fast-talking figure bustling through the huge glass entrance, past the flickering candles and the tribal carved chairs, breathing in the spiritual calm of a spacious cathedral dedicated to simple, fine taste, fingering the black walls, revelling at the suspended white stone floors, touching the gold-leaf painted staircase, catching her own image in the huge mirrors.

Donna Karan was in town to see her new, eponymous London store open in New Bond Street. It's the first ever devoted to her collection, the pride of a woman who is fast becoming the most important female designer in the world. After all, she dresses Bill Clinton and would, if America had a female president, almost certainly kit her out too. There she was on day one, preaching to dedicated admirers the Karan Creed, her love of sensuality, of comfort, of luxury and ease, the smells, touch and femininity of a style that seems to embrace women, hug their very souls.

For Donna Karan has an unusual relationship with her customers. Often the passions of fashion designers can be enthralling, courting a woman client with the promise of transformation into another being, teasing her that in her body resides the finest beauty. Then the affair turns sour when the wearer realises the designer is really in love with a different woman, a mythical Venus who barely exists except as a freak accident of nature.

Karan is different. She's a real woman, with a generous, womanly shape. An exuberant, warm, volatile New York Jew, with few enemies, she designs for bodies as they really are, creating garments that glide over the bumps and lumps. "She makes clothes you don't have to be a model to wear," says Vogue's Lisa Armstrong.

"Her great strength is that she is absolutely certain about her neuroses," says Ilse Crawford, editor of Elle Decoration. "She has all the neuroses of a woman who looks in the mirror and thinks, `Yuk'. Her clothes are designed to flatter women with hips, which most women think they have, even if they don't." They are "problem-solving clothes" comprising essentials that can be worn in different combinations to suit every occasion. She wears only her own designs. And she is a saleswoman with a common touch that wouldn't be out of place in an east London market. As she rolled into town, opening across the road from Valentino, a few doors down from Ralph Lauren, Donna Karan was as good as saying to British women: "Hey, sisters. Forget these guys. Look at me. I'm like you and I look and feel great. Let me do it for you."

Her store is like something transported from Madison Avenue, a palace devoted to cosseting women - and men - in a mean city. September rain may have lashed summer tans this week, thunder disturbed the calm in Tuscan villas, but Donna's refuge for the rich is there to massage the spirit with finely-cut cashmere.

The message of her imminent arrival had been borne by friends in the preceding weeks. Demi Moore and her husband, Bruce Willis, have been wearing her clothes all over the pages of the glossies since August, looking sexy, sensual and elegant, a little dishevelled, even slightly shagged out, as if they have just slipped out of a luxurious bed in which sleeping was a secondary consideration. You can sense the eroticism, the intimacy of a couple, who may be film stars, but who are also real people: Demi and Bruce are genuine husband and wife. Demi's looking tired and sometimes vulnerable. She's got a bit of a tummy. But the clothes still look fabulous.

This is the type of intimate, emotional advertising Donna Karan is using to draw Britons into her world. She is already the best girlfriend of many American women, the designer who gave them "the body", an all-in- one undergarment with popper buttons on the crotch, the perfect canvas for her simply-cut jackets and dresses, of soft pliable materials that melt around the individual. Her hosiery is a marvel of engineering, smoothing, supporting and sheering in all the right places.

Her clothes speak to the aspiration of the modern, female professional who has matured since the power-dressing Eighties and now needs a subtler, more under-stated expression of status. She doesn't have to dress like a man. Nor does she have to be a sexual star, sparkling among the males in a short skirt. She needs to be comfortable. lightly dressed in clothes that will look good in the office, and still pass muster at a dinner party.

Most important, Karan's personal life strikes a chord with those scaling fresh pinnacles in gender politics. Her father was a tailor and, although she grew up in a well-off Queens suburb, she is a self-made woman, who learned the art of salesmanship working in a shop at 14. Now, at 47, Donna Karan is mistress of a business empire that is valued at $275m, though founded barely more than a decade ago.

She has had to juggle family and career. Married at 19, she had her first child at 25, days before her boss and mentor Anne Klein died of cancer, leaving her as heir apparent to the fashion house. Karan nearly gave herself a nervous breakdown, but produced a fresh collection in six weeks and then moved on to creating her own fashion house.

Her first marriage did not survive her success: she is now married to Stephan Weiss, a sculptor who has been a key figure in the business and who recently recovered from lung cancer. He calms her, she says, keeps her exuberance down. A good Jewish mother, Karan remains plagued by guilt over not spending more time with her daughter, Gabby, who is now 22 and involved in the business. She speaks of herself as the dutiful mother of the company, and of her employees as her children. She'll be playing Earth Mother again at a huge splash party next Thursday during London Fashion Week, aimed at raising donations for cancer research.

These days, Donna Karan has all the accoutrements of the successful New Yorker - an all-white beach house in the Hamptons, a seven-room Manhattan apartment, friendship with Barbra Streisand. She's a New Ager and has spoken, to the concern of the stock market, about her reincarnation and seven past lives, including one as a painter for the Medicis.

But success has not apparently turned her into a shiny, brittle product. Ilse Crawford recalls a visit to her beach house. " When we got there for the shoot, I had remembered everything except some knickers. There I was in the middle of Long Island and nowhere to get knickers. She instantly riffled through her drawers and came out with a pair of hers, washed, but they had been used. I thought, crikey, this is the sort of thing an old friend does."

Fashion history will almost certainly judge Donna Karan as the executive woman's champion, who gave the new woman clothes in which she could feel easy anywhere. But that would neglect her triumphant entry into men's wear. She is responsible for some of the best-selling men's suits in America, all designed in simple style, with her husband Stephan in mind. There is, as with all Karan's best work only one problem. Expect to pay pounds 2,000 for her finest suits, for men or women, at the new elite store. The rest of us, at a pinch, are more likely to be able to afford the pounds 500-600 a suit at her more downmarket DKNY outlets. Or if that's too much, there are always knee-highs for pounds 6.50.

Karan is reaching for fresh accolades. She is, like Ralph Lauren, demonstrating how open Britain and Europe is to mass fashion export from America. She brings New York to London in her advertising - yellow cabs, glamour, glitz, the harshness of a city perched on the eastern seaboard, prey to the wind and ice of winter, the overbearing humidity of summer. For the past two years, DKNY, her in-your-face, hip store, located down the road from her new emporium, has been selling sports-wear, jeans, kids' clothes and some of her cheaper collection lines.

It has captured the British imagination. Furniture and a host of lucrative lifestyle spin-offs could come next. The big test now is whether British women will follow their American sisters and fall in love with Donna. Do we want to be Demi and Bruce?