I made David clean up his act

She says he hated her fussing over him while he spent a few weeks recovering at their downtown apartment. "I was like, 'Don't walk, don't move' and he kept saying, 'I'm not an invalid,'" she says, laughing. "He stopped smoking, he used to drink a lot of coffee and he only drinks decaf now, and there are no more fry-ups. He feels the difference, and he's glad it made him stop smoking because that was his last vice - he couldn't stop. He said it was the hardest thing to give up."

Did she dare to think of life without him? "Obviously when something like that happens you do think [that], but I could see the difference in him within weeks. This also comes with age, but you're more aware of mortality. You realise how fleeting life is, that you are mortal and something could happen at any time."

Not that Bowie's heart operation changed much for the couple. He is still writing and performing, while Iman has signed a deal that will take her cosmetics brand across the world. "We're not retiring people," she says when I ask if they wouldn't rather have a nice, easy life with their estimated £120 million combined fortune. "And anyway, I do have a nice, easy life."

Maybe it's age or maybe it's because they've both had their hedonistic lives - while Bowie was Ziggy Stardusting it up, his future wife, a fixture at Studio 54, once said she indulged in "everything, the cigarettes, the champagne and the coke became part of the fashion show" - but now Iman insists that they're "kind of really boring. A typical day for me is to get up at 6.30am, have breakfast with Lexi, take her to school, go to the gym and come to the office. We'll be at home in the evenings, I'll always cook."

At weekends, they take their daughter to the park or the zoo, or sit in cafés (where New Yorkers are far too cool to bother them). Evenings are spent meeting friends for dinner or occasionally going to the theatre or to one of New York's glittering fundraising dinners. They don't have an entourage, only a nanny ("I'm 50, with a five-year-old, I need a nanny!" she says).

Iman has just launched a range of make-up kits to complement her new book, The Ultimate Beauty Guide for Skin of Color. In the book, there is a photograph of Iman as a child. When you see the sweet young face of the Somali girl yet to become beautiful, the round cheeks yet to morph into those cheekbones, you realise quite what a journey Iman's life has been.

She was born in Somalia in 1955 but spent her early years living in Ethiopia with her grandmother. After the 1969 revolution, politically active neighbours started " disappearing" and Iman's father, a diplomat, became worried. The family left in the middle of the night and fled to Kenya.

"I think it was the hardest for my father," she says. "Our lives changed dramatically. From being from a family who had something, now he couldn't afford to pay for our education. We went from being the children who were taken to school by drivers to refugees."

Iman went to study political science at Nairobi University and took jobs waitressing and translating tourism brochures (she speaks five languages, including Italian and French) to support herself.

It was when she was on her way to a lesson one day that the photographer Peter Beard stopped her. "He asked me if I'd ever been photographed. I thought, 'Oh god, here goes another white man who thinks we've never seen a camera.'"

He sent the photographs he took of her to a model agency in New York and they immediately took Iman on. By this time, she had married a hotel worker but the marriage wasn't working. She left for New York without telling anybody.

The first Iman's parents knew of her fame was reading about her in a copy of Newsweek (Beard concocted the story that she was a poor illiterate goatherd). "My dad saw it and was furious, he tried to get me to come home, saying I was wasting my life. He thought modelling was little short of prostitution." He wasn't placated when, within three months, she had made enough money to take care of the whole family (her parents now live in America).

After the initial hype had died down, Iman was aware that people's interest in her only went as far as her exotic beauty. "If I was going to stay in this business, I wanted to make a place for myself. I didn't just want to be hauled in if a magazine was doing headgear or ethnic jewellery," she says.

"It was frustrating. I refused to take certain jobs. If a magazine needed a black model, I would say, 'Find someone else.' Or you do the same advertising job and you get paid less than the white models, then no, I wouldn't do it. I had to stand my ground."

By the time she retired in 1989, she was the first black model to front the big advertising contracts and the first to command fees of £20,000 a day.

It must be hard to reconcile her fabulous wealth with that of the average Somali. " Absolutely. I'm careful with Lexi in that way. There are so many people who don't have basic needs, so I don't think I can justify buying a five-year-old things from Prada. She's already privileged, she doesn't need me to spoil her."

Can she ever see herself going back to Somalia to live? "No, I'm definitely Somali but my home is New York," she says. "But I would like my parents to be able to go back. They would love to be buried there. They talk constantly about Somalia." And then, that beautiful face cracks ever so slightly and Iman suddenly looks as if she's about to cry.