Hollywood: Next The Sea

'Paul Simon was sitting in our restaurant eating and I had no idea - someone had to point him out to me. Then, another time I was out at the dock getting supplies from the boat and this lady bounces up to me and says, "Hi, I'm Sarah Jessica Parker. We are so looking forward to coming for lunch with you!"

It's little wonder that that Sandra Wallace - owner of Anguilla's gorgeous Scilly Cay desert island seafood restaurant - does not always notice a superstar diner in her midst. Brad Pitt, Courteney Cox-Arquette, Kevin Bacon, Janet Jackson, Uma Thurman and Robin Williams breeze into Anguilla as frequently as the trade winds that cool this Caribbean island. It's the celeb-obsessed teenager's idea of heaven.

Currently there is no island more "in" for the Hollywood A-list than Anguilla, which lies between the Virgin Islands and Antigua. Not that you would know it was hip from first sight. Apart from the line-up of private jets at Wall Blake airfield, Anguilla is more stealth wealth than conspicuous consumption.

But this is not Barbados nor Mustique. In Anguilla, rubble and rusting cars are not swept up just to please the visitors, and The Valley, Anguilla's capital, is a motley collection of weatherbeaten shops and businesses built to withstand hurricanes, not to lure American Express black card holders.

Anguilla's real draw is its coastline. You'd need to stay on this lizard-shaped isle, which measures 16 miles long by three miles wide, for a month to experience all of its beaches. For those with limited time, Sandra recommends Shoal Bay, Meads Bay and Crocus Bay.

Giving my kids the island map and with me at the wheel of our jalopy hire car, we took her advice and spent carefree hours sampling Anguilla's white stretches of sand. Shoal Bay came out top; a close second was Little Bay where we took a picnic by boat and spent hours in a real-life episode of Finding Nemo.

"It's not just the beaches that lure the celebrities," says Sandra. "This is one of the few places in the world where the stars are not disturbed. Even when Jay-Z came here, the Anguillans were happy just to stand and watch him, not bother him. For movie stars, Anguilla is heaven."

It is heaven not only for celebrities. The next day, from where we are sitting outside Gwen's Reggae Bar, to the hook of sand 300 yards away at the other end of Shoal Bay East, there are just eight people. That includes the four of us. "If you have to hear someone else talking on a beach then it's a crowded day," says the barmaid. At that point my kids fling themselves noisily into the surf. I think about asking them to pipe down. But what's the point? There's no one else in earshot.

Despite the fact that most visitors are American, the feel of Anguilla is unmistakably British. Kids play cricket on any open space they can find. The cars drive on the left. Pictures of the Queen's last visit in the 1980s are not uncommon.

Something, fortunately, Anguilla has not inherited from us is its cuisine, which is spectacular. Much of the time we barbecued fresh mahi mahi on the terrace above Sandy Ground beach. But it's also worth splashing out in one of the island's restaurants, even if they are quite pricey. All the restaurants we went to welcomed children with open arms and tailored their dishes to childish palates.

The best food we found was at Sandra's own Scilly Cay and, for dinner, The Straw Hat, stuck out majestically on stilts above the Caribbean Sea. Chef Marc Alvarez's menu uses the best local ingredients cooked with a mix of Caribbean and cosmopolitan flair.

"The food is whatever you want it to be," explains Sandra. "One of my favourite things is to take a charter boat to Big Scrub Island, have a picnic with fresh local fish and go swimming. But then there are fabulous restaurants like the one at Altamer or Tasty's or Blanchards."

The restaurants serve another purpose. They are about the only lure to get the celebrities away from their £50,000-a-week villas.But whatever you do or wherever you stay, if you do eat out, just make sure you pay attention to who is at the table next to you.

Trailfinders (0845-058 5858; trailfinders.com) offers return fares to Anguilla starting at around £620 from London Heathrow via Antigua with British Airways and Liat.

The author and his family stayed at Spyglass Hill villa (001 264 497 3666; spyglasshillanguilla.com). Daily rental of a villa sleeping eight costs from £700. While it's perfect for a family it's unsuitable for small children. For more information on Scilly Cay, see scillycay.com. For more information about Anguilla see anguilla-vacation.com and anguillaguide.com