Anguilla gave up dependence on fishing and salt exports in the Eighties, and decided to cash in on its natural advantages and our relentless quest to discover the last bits of paradise. Named after its eel-like shape, Anguilla is not everyone's idea of a Robinson Crusoe retreat even though it is three miles wide by 16 miles long. It is a scrubby, low-lying coral island, exposed to the prevailing winds. There are few coconut palms swaying in the breeze, no cascading waterfalls, and a distinct lack of tropical trees groaning with exotic fruit.
But what it does have is 30 exquisite beaches - one for practically every day of this month. The names are as seductive as any in the Caribbean: Captain's Bay, where turtles come to lay their eggs; Rendezvous Bay; Cove Bay; Crocus Bay. Some are just small stretches in dramatic settings; others go on for miles, gently lapped by azure waters. All the ones we managed to get to in seven days had dazzling white sand.
Shoal Bay must be one of the best beaches in the entire region, with a choice of restaurants and good local music at least twice a week, but I never counted more than six people in the warm turquoise water at any one time. So if your idea of a good beach is one where you have to pick your way through lobster-pink bodies pressed between sea and land, you will feel lost here.
Anguilla is strictly a place for those in the know. The people you meet here are connoisseurs of remoteness. No backpackers, and only a few day- trippers (from neighbouring French Saint Martin). The cruise ships have been all but seen off and there are no cheap package holidays. The tour bus hasn't yet put in an appearance, and the locals just let you get on with it. We got the message as we stepped off the 19-seater plane (no Jumbos here). I had to round up a porter to get our luggage and, once we were outside, there was no string of soliciting taxi drivers.
In fact, nobody ever tried to sell us anything or take us anywhere. Tourism may be the biggest money-earner here, but most of the islanders seem to have better things to do. Only Raymond on Shoal Beach would gently and smilingly ask for a random sum to park us on comfortable deckchairs under some shady parasols on the "best" bit of the beach.
And that is the reason to come here - for a completely hassle-free holiday. It's something well-off Americans have learnt.
And they are prepared to pay big money for it. A double sea-view room at the secluded Malliohuana Hotel costs $650 (pounds 420) a day at this time of year, and the most modest rate at the equally elegant and beautifully designed Cap Jaluca Hotel is $745 (pounds 480). Suites cost in the region of $2,000 (pounds 1,300) a day.
Down at Island Harbour at the other end of the island, Smitty - the legendary inventor of the beach bar in Anguilla - proudly displays a multitude of snaps of himself with famous but shy paradise-seekers. "The only people who wouldn't go unnoticed are the Chicago Bulls," one customer assures me. And Smitty is the man who must take the rap for that. It was he who introduced TV and American sport to the locals, exchanging a quiet beer at the end of a day's fishing for the cheering and booing at the greats of basketball and baseball.
Back in 1978, when he put his paradise hut down on the sandy shore, there was no electricity, running water or luxury hotels. He got a generator, played loud music, introduced a barbecue for cooking the island's sweet crayfish and lobster, and just watched the customers roll in.
With few cars and even fewer paved roads it was a long trek, but they came - and still do - for his homilies ("Every day is a wonderful day when you are alive"), for the warm hospitality, and for the assurance that Anguilla is one of the very last havens you can visit.
Anguillans are happy with their expensive brand of top-of-the-market tourism, with the island's reputation for haute cuisine and simple exclusivity. It's what brings top chefs such as Marc Alvarez from New York to perform culinary miracles with freshly caught swordfish and tuna. He gets foie gras for his Straw Hat restaurant from France, lamb from Miami and filet mignon from the Mid-West. That means that the prices are high - as high as in London. And that's true wherever you go, from simple Smitty's to smart Covecastles, where the chef is French.
When I lived in the Caribbean all I knew about Anguilla was that it was the most northerly of the Leeward Islands and formed part of a three-island entity with St Kitts and Nevis, which lie 70 miles away. But in 1969 Anguilla shot to international fame when the islanders rebelled against independence under Kittitian dominance, in favour of colonial rule.
The UK prime minister Harold Wilson sent in 315 paratroopers, helicopters, the Royal Navy, the RAF and a stand-by detachment of London policemen to put down what the locals call their "revolution". British papers parodied Wilson, and the island's small but excellent Heritage Collection Museum has some highly amusing pictures of the British bobby on beach patrol, making friends with the welcoming revolutionaries.
Now, Anguilla is one of Britain's five Caribbean Overseas Territories. It has 10,000 people, a governor, no army, no income tax, no crime, little unemployment and an abundance of peace, tranquillity and the good life, even if it is bottom of the Fifa league. Paradise indeed.
Marina Salandy-Brown paid pounds 590 to fly to Anguilla via Antigua through Flight Connections (0171-344 0101 and 0161-839 5111). Easy Corner Villas (001 809 497 6433/6541) cost from $160 (pounds 100) per night for a one-bedroom villa and car rental costs $40 (pounds 25) per day or $240 per week (pounds 154). For more information, contact Anguilla Tourist Board at Windotel, 3 Epirus Rd., London SW6 7UJ (0171-937 7725 or: atbtour@anguillanet. com). A good read: 'The Northeastern Caribbean' (Cadogan, pounds 9.99)