The problem is, the more food we order, the less chance busy Claudia will have to lay down that skillet and pop up from the grease-pit to say "Guten Tag!". And Naomi - she's too tied up polishing the cutlery. And Elle - Elle is printing the T-shirts in a factory in Omaha. Still, any minute now.
While we wait, we may browse the menu. Each model has created a special dish. Claudia has chosen apple pancakes served warm with caramel sauce and cinnamon ice cream ($8.95), Elle has picked shrimp on the barbie with a tomato-corn salsa ($8.95), and Naomi has delved deep into her Streatham childhood to contribute fish and chips ($8.95). Each of the girls have said that, despite appearances to the contrary, they spend large parts of every day eating these items, especially before an important shoot.
Most diners this afternoon have gone for the cheeseburger, but it's a hamburger with pretensions, for the cheese is havarti. The turkey meatloaf is also popular, along with the Thai spring rolls and the sorbet soup and the "Fashion crab cakes" and "Fashion cobb salad" and "Fashion tarte" - a handsome mix of the mouthwatering and the meaningless. But, strangely for a restaurant, food is not really the thing here.
Conceptually, the Fashion Cafe has a unique beginning. The story is told of how a 28-year-old entrepreneur called Tommaso Buti married Sports Illustrated Swimsuit Special cover girl Daniela Pestova, and she introduced him to her friends, and these friends were among the most beautiful and wealthiest in the world, but their lives were hollow. What they wanted was a place to call their own, a place they could hang out and admire great clothes. First they wanted New York, and two weeks ago it was announced that they wanted London too, and a site had been found for them in Leicester Square, where it was hoped Fash Caff 2 would open either next autumn or spring.
But now that their dream is a reality, we find that like so much in fashion, the reality turns out to be full of little deceits. The Fashion Cafe has some very interesting clothes in it, but they are not on the customers. Above my head, in the Paris Room, is Madonna's Gaultier bustier; to my left is Audrey Hepburn's Givenchy dress from Breakfast At Tiffany's; on the right the tall shoe Naomi Campbell fell off for Vivienne Westwood.
But it is not a chic place. The Cafe has only been open since the beginning of April, but already word of its existence has filtered down to almost all the world's most wide-arsed tourists. This is their place now, and their only serious competition for tables comes from male horn-dogs out for a good ogle. The place seems to have bypassed its hot period.
Not that it isn't doing great business. I have been joined at my table by Amy Newman, responsible for the Cafe's public relations, who tells me that people are more than happy to queue outside, behind ropes, for 40 minutes to get a chance not to see Claudia; the wait sharpens their appetite, heightens their anticipation, gives them a chance to look in at the neatly positioned merchandise shop (T-shirts $16, special leather jackets $1,500). The entrance is through a mock giant camera lens. Then you're greeted by video mannequins, which have the projected face of our three supermodels. This is not fully operational yet and neither, on my visit, were the many video screens that should have been showing catwalk highlights from the recent shows. When these get fixed there are plans to erect a runway through the restaurant, where live models may perform and magazines may conduct fashion shoots, if, by some terrible fate, all the flights to the Bahamas are full. Amy says that she hopes marketing agencies will bring their girls in, but she must be crazy.
She also says, "Elle announced that for her the Fashion Cafe stands for five 'M's. Mood... Menu..." She is interrupted by the waitress announcing specials, in which the word julienne features prominently. I order steak, which comes very fast and is very good, but has a wooden stick in the middle with yellow cellophane on top. We are then joined by Kelly Rae, who has helped curate the garments on the walls. She says that most designers were happy to donate or lend their wares. Some saw it as an honour. Azzedine Alaia appeared to be a lone dissenter when he said: "Putting dresses in display cases seems pretty strange to me. I wouldn't do it even if they paid me royalties."
The Cafe occupies part of the Rockefeller Center, many blocks from the genuinely hip Odeon or Bowery Bar downtown. But it is near several other theme restaurants - the Hard Rock Cafe and Planet Hollywood, of course, but also the Harley Davidson Cafe (big loud bikes overhead), Jekyll & Hyde (star attraction: a Frankenstein) and, coming in the autumn, the Motown Cafe and the TV Cafe.
Bruce Miller, one of the Fashion Cafe managers, has worked at both the Hard Rock and "Planet", but he says this new place is his favourite, not least because the food is more varied, the crowd older and more sophisticated. He is candid about his ambition: more seats, faster turnover.
"We have 240 seats. We're doing 1,200 to 1,300 customers every day. I'd like to get it up to 2,000. We hope to get things running smoother so that people won't spend so much time in the restaurant." Accordingly, the appetisers must arrive eight-to-ten minutes after ordering, the entrees after 18. "The average stay is about one hour 15 minutes," Bruce says. "But an hour would be nice."
I ask him the big one, about whether the three models are just a front, being paid for their time and endorsements. He says they are very involved. "I understand they have invested money. And only yesterday Elle was in here, passing on some hints."
"She went to the kitchen and said the fries weren't quite right, and that her shrimp in her shrimp on the barbie weren't big enough."
He talks about the opening party. Duran Duran played. David Copperfield pronounced it "magical". Minnie Mouse turned up, in the words of a Disney spokesman, "to see Claudia Schiffer". And Claudia and the other two turned up to say they were making "all the decisions" themselves.
Other partygoers saw it differently. "The girls' diffidence pervaded the entire event," says Roger Friedman of New York magazine. "Elle gave a quote to the local tabloid saying she wouldn't even eat there. It was a disaster."
Immediately the manager left I was to have been joined by Barry Depaulo, executive chef. He doesn't show.
"The chef hasn't come yet?" the PR woman asks.
"Perhaps", I offer, "he's enlarging his shrimp."
"I can't believe it," she says, putting her hands to her mouth as if this was the most remarkable thing since the polio vaccine. When he does appear he's carrying a thick computer printout. "I know how much it takes me to buy and sell each Thai spring roll," he announces. He says Claudia's pancakes are the third most popular dessert - well over 60 a day. He says the wooden stick in my steak is to show how well done it is - a red stick is rare, yellow medium-rare, right up to crispy, which is blue.
"People are laughing about it," says Alix Browne, a fashion writer on Harper's Bazaar, "but they don't want to be too cruel because it is Claudia, Naomi and Elle." But last week she went to eat there "for a lark" with some friends from the magazine. "We were the most fashion-related people there. We kept on asking where Claudia was, and at first the waitress said she was in the kitchen. Then we asked again, and the waitress got a bit tired of us. We were surprised how big the portions were. Models just don't eat that - they should just sell coffee and cigarettes and alcohol."
After London, there are plans to open Fashion Cafes all over the world: next will be Madrid, Las Vegas, Sydney. Diners do seem to like the concept. A woman who came with her daughter told me it was great fun; a man from Germany said that even the waitresses were beautiful; a woman from Manhattan said that this was the closest she had ever got to the fashion world.
And they hope, perhaps, that some of the ersatz glamour will rub off, and that they'll gaze enviously at the narrow waistlines in the glass cases, and they'll order another apple pancake, and they'll glide back out through the camera lens feeling a little more like Kate Moss and a little less like the overladen 18-stoner that walked in 75 minutes earlier. The reality suggests they have as much chance of becoming Kate Moss after eating at the Fashion Cafe as Naomi Campbell has of becoming a belle lettriste after swanning through Waterstones.
A few days after my visit, Elle Macpherson called up. She said she was thrilled with the progress of her project, and expressed particular delight in the quesadillas and the chicken wings ("and of course I get great service!"). As a businesswoman, she said she was fascinated with the steady growth of the theme catering industry. The hardest thing was "convincing the designers that they wanted to put their clothes in a restaurant".
I wondered about her own personal financial investment. She said: "I think that those kind of things are the kind of things I don't like to make public." Later she said she was sorry, but there was a gulf between what she wanted to say, and what she should say. "What I should say is...well...no... I'm trying to be accurate without denouncing any of the glamour."
I asked her about this glamour, and whether she hoped the fashion crowd would hang out at her joint. The Cafe, she explained, "is exactly what it is. We never really wanted to make this a trendy place."
The following day, Stuart Cameron, her manager, called me. "Elle told me that she told you that the place wasn't trendy," he said. "I wanted to clarify exactly what she meant by that. She didn't mean it wasn't fashionable, she meant that it wasn't supposed to be a fad, not here today and gone tomorrow."
Another call followed, from Amy the PR woman. She claimed to have mastered Elle's five "M"s. "Mood, Menu, Merchandising, Memorabilia and...oh shit!..." She disappeared. What could the final M be? Models? Moschino? Surely not Malnutrition? She rustled through papers. In the background, in a mantra, she was saying "mood, menu, merchandising..." She came back to the phone. She had the fifth M.