"There's a must-have pointed-toe court shoe at pounds 160 and they went straight away - we're waiting for a second delivery now," says a spokeswoman at the Sloane Street branch of the upmarket Italian label, Prada. "And our beaded skirts, dresses and tops went like that," she adds.
It's the same story in the men's department where customers often have to leave their credit-card details and pray that a sympathetic salesman will call if a garment in their size arrives. The three-button suits at pounds 800 and roll-neck sweaters at pounds 280 sell out as soon as they arrive. Apparently the keenest customers phone the Prada shop within hours of the company's Milan catwalk show finishing, demanding to know when their favourite items will be in stock (the answer is not for six months).
Harvey Nichols, the leading fashion retailer, says that its stock of hipster trousers by the Belgian designer Ann Demeulemeester was snapped up within 48 hours of going on sale, and that the additional stock transferred from its Leeds branch lasted only hours. Also gone are all the pounds 85 side- split mini-skirts from Miu Miu, an off-shoot of Prada. And if you want shoes by America's Richard Tyler or anything by Helmut Lang, Harvey Nichols says you'd better hurry.
Over at Liberty, the Regent Street department store, they are also facing sartorial shortages. Spokesman Nicholas Sullivan says that the controversial British designer Alexander McQueen (he's the man who made those bum-revealing trousers) has been a huge hit. "We ordered 15 of his black sheath dresses with rose embroidery. They went on sale at pounds 259 on a Tuesday and were all gone by the Thursday and we can't get any more. We are experiencing the same thing with Dries Van Noten. Anything by him is just walking."
Browns, London's celebrated designer boutique, has also been besieged by clued-up shoppers. Spokeswoman Bomi Odufunade says there is nothing left by the young British designer Hussein Chalayan and she adds that men have bought up nearly all of the slinky Helmut Lang line.
Shoe designer Patrick Cox already has waiting lists for much of his autumn range: if you want the peep-toe sling-backs or the red boots embroidered with a dragon - yours for pounds 320 a pair - you'll have to be patient.
Even companies offering copies of designer looks have been unable to satisfy demand. Office, the high-street shoe chain, sells a pointed-toe ankle-boot that looks, even to those in the know, like Gucci. Within days of them going on sale, every branch sold out and all have long waiting lists. Sara Hill, the company's marketing manager, says "it has just gone completely mad, we've been overwhelmed by the demand. I've had people phoning up begging me to get them a pair."
If things continue like this, expect fashion ration books any day now.