The mile-long white sand beach of the Cap Juluca resort on the tiny Caribbean island of Anguilla is like a second home to some of the capital "A"s on the Hollywood A list. At the very least, I expected to find myself sharing the odd cocktail or two with Tyra Banks. Even Janet Jackson, another regular client, would have done at a push.

Initial signs looked good. From the moment you drive through the gates of the resort, it is easy to see why so many celebrities choose to descend here. Built on a small cape jutting out from the predominantly flat and arid island, 18 private moorish-style beachfront villas line the sparkling aquamarine ocean. There are three restaurants, two of which are built on a dead coral reef so that you can virtually dip your toe in the water while enjoying haute cuisine, while a third, located almost on the beach, serves up traditional Caribbean food.

The villas are sumptuous in the extreme. For the average punter (not that there are many of those at Cap Juluca), there are beautiful unfussy bedrooms with wooden doors opening on to expansive balconies with unobstructed views of the beach. In a touch that lets you know you are staying somewhere really special, the maids serve breakfast on the balcony every morning, so you don't have to bother getting dressed up for breakfast (believe me, Cap Juluca has the sort of clientele who would get dressed up for breakfast).

But it is the bathrooms - in which any self-respecting rock star would be happy to overdose - that really take your breath away. Enormous mirrors cover one wall with his and hers sinks and a bath and shower big enough for five or six groupies while glass doors open out on to a private, walled-in sunbathing area (going topless is illegal on Anguilla). Believe me, you could have a very nice holiday without ever leaving the bathroom.

For the seriously moneyed and seriously famous, there are a selection of private villas with their own swimming pools - apparently, so my sources told me, favoured by Puff Daddy and Jennifer Lopez (when they were still together).

Part of the charm of Cap Juluca - and indeed the whole of Anguilla - is the way in which everybody tells you they could not possibly divulge anything about the celebrities who visit as it would be a breach of trust. But when everybody else has their back turned, they really cannot wait to fill you in with the juicy details, from the fact that Steven Tyler of Aerosmith has the anti-social habit of wailing like a banshee from beside his private pool, to the supermodel Naomi Campbell's penchant for putting on impromptu catwalk shows for the slack-jawed gardeners along the resort's private road. "Man, she knew what she was doing," one of them told me, describing the T-shirt and buttock-exposing cut-off jeans she was strutting in.

But while all the talk might have been of celebrities, the stars themselves were doing a pretty good job of keeping a low profile. Despite numerous walks along the beach peering below umbrellas and sun shades and trying to look through the windows of the private villas, there was not a famous face in sight.

Part of the reason for their apparent elusiveness might have been down to a touch of hurricane nervousness. The resort only re-opened late last year after being closed for 12 months when it found itself on the wrong end of hurricane Lenny. "We got caught with our pants down," the general manager told me, describing how the hurricane appeared to be heading away from Cap Juluca before turning around and catching the hotel head on. The buildings just about survived intact, albeit a metre or so deep in sand, while the startled guests sheltered in the main reception building.

A couple of million pounds worth of re-decorating later, (including building a concrete spit that has now been covered with sand along part of the beach to protect against future hurricanes) and the resort is back in business.

Even the location of Anguilla exudes exclusivity. The island is the most northerly of the Leeward Islands, lying 70 miles to the north-west of St Kitts and five miles to the north of St Maarten. There are no direct flights from the UK and the island's tiny airport can only cater for 50-seater planes, which has kept away the mass-market hotels. Instead, the voyage of choice to the island is on small private planes from the Caribbean's international airports.

Having failed to track down any famous faces at the resort, I decided to take my search further afield. A likely venue is Scilly Cay, a tiny little island that houses one of Anguilla's best known restaurants - called not surprisingly Scilly Cay. Walk to the end of the jetty, wave at the boatman who speeds over to pick you up and take you to the tiny coral and sand islet. At $50 a head it is not cheap but the lobster (you can pick your own fresh from a tank on the beach) is the only thing to have.

Unfortunately, we were 24 hours early. They were expecting a big celebrity the next day, Eustace, the restaurant owner told us, but refused to elaborate. "Richard Gere? Kevin Costner?" I suggested (both of whom have apparently regular visitors to the island) but he wasn't letting on.

The restaurant is only open during the day, so if you are looking for an evening meal, head for the Koal Keel restaurant, situated in the second oldest building in Anguilla, the warden's house. The food was excellent, but the definite highlight of the evening was tasting the enormous selection of rums kept in the inviting "Rum Room", containing everything from a bog-standard bottle of Bacardi to a very palatable 50-year-old bottle of the local Anguillan variety.

In a last-ditch attempt to spot some celebrity talent, we headed for the island's nightlife hotspots in Sandy Ground, a small village that used to be the centre of Anguilla's salt industry. The Pumphouse, a cozy pub with nightly music, and Johnno's Beach Stop, a club that plays soca, reggae and jazz, are the two most popular, although neither can really claim to compete with Jimmy'z in Monte Carlo or Viper Room in LA. Unfortunately, any celebrities who might have been on the island seemed to agree.

Time was running out, but finally on the last morning in the resort there she was, a vision in a white bikini with a towel wrapped round her waist. Yes, it was Charlie Dimmock, the most famous gardener ever to be plucked from the obscurity of Mill Water garden centre in Romsey. Oh well.

Way to go

Seven nights' B&B at Cap Juluca costs from £1,755pp with Abercrombie & Kent (0845 0700613, www.abercrombiekent.co.uk), including British Airways flights to Antigua, and an onward connection by Liat to Anguilla.