Barbados, with its true winter "season", is a good contender. "Our season runs from mid-December to mid-April," says Trevor Ramsay, owner of the Treasure Beach Hotel on the western side of the island. "It's a little more, well, polished than the season in resorts in places like Africa." The hotel, which consists of 25 private suites, surrounds a pool and garden blooming with hibiscus, bougainvillaea and jasmine. You can laze on the beach every day, and drink cocktails and dance to calypso bands every night. Best of all, between November and March, there are no kids under 12. But is there glamour? "Oh yes, we have the stars here. Dave Allen, Brian Ferry. And Mark Pitman was married here. It was in Hello!."
Well, quite. But I don't want to have my holiday wrecked by invasions from Hello!. I want private luxury, true get-away-from-it-all glamour. So I flew away from Barbados in a nine-seater Cessna and went to the tiny island of Mustique.
There's just one landing strip, carved out between high, heavily wooded mountains. There are no night flights; in emergencies, people on the island simply drive along to the airport and line their cars up with the headlights full on, to provide illumination. The airport itself is a small hut with a bench for Customs, and, weirdly, a lending library, two bamboo bookshelves stacked with titles such as Fishing with Ray Bergman. And that's it. Celebrity marriages? I don't think so. The paparazzi have their cameras removed on arrival. Welcome to the most exclusive island in the Caribbean.
Mustique was put on the map by Princess Margaret who was given a plot of land here as a wedding present by Colin Tennant. Tennant had bought the three-mile long island in 1959 for pounds 43,000. It was a lot of money for not very much; an empty wilderness with no fresh water and a rampaging population of mosquitoes (hence the name). But Tennant had a vision and in subsequent years he managed to woo the talented, the artistic and the mega-rich from all over the world in order to achieve it.
Margaret built a villa on her plot of land and brought her social set along for Christmas. Gradually, they too bought their own plots of land and built their villas; and thus began the history of Mustique's glittering exclusivity. You can practically smell it on arrival. Brushed beaches, clipped grass and blue skies frame multi-million dollar houses in a guaranteed mosquito-free atmosphere thanks to frequent visits from sprayer planes. The houses aren't built on the beaches. They don't need to be. These people have their own pools, their own jacuzzis; hey, they even come equipped with golf-simulation cinemas equipped just so you can practise your swing. Who lives here? Oh, the Jaggers, royalty, Swiss bankers. Serious money. "Didn't you know that David Bowie's just sold up, for four?" Four what? Thousands? Hundreds of thousands? "No, stupid. Millions," In Mustique, everyone speaks in multiples of six zeros.
For mere mortals, Mustique is probably the best place in the world where you can still play at being a superstar for a week. More private club than resort, this is one place in the Caribbean where parties from cruise ships are not welcome. There's only one hotel, for a start. The Cotton House, an 18th-century coral and stone cotton warehouse that was taken over by Tennant and used as his HQ in the Sixties, is now a deluxe hotel and centre of the island's social scene.
Decorated in a somewhat outrageous style by the theatrical designer Oliver Messel, the Cotton House now has 20 suites dotted about the grounds surrounding the main building, and a reputation for service that relegates the average five-star British hotel to something approximating a motorway service station.
Oh yes, there's all the regular luxuries like tropical flowers in the bedroom, ice-buckets changed regularly and cocktails on arrival, but lunch brought by hand to whichever beach you desire? Surely some mistake? Not at all. If you wish to pretend that you're in some Fleming-esque fantasy, you can do so. A brief word at breakfast by the pool is all that's necessary. So after a morning swimming, snorkelling or going for a gallop along one of the island's pure white, combed beaches, you simply plonk yourself down at the appointed site with a towel and plenty of factor 25 and wait for nourishment. At the pre-arranged moment, it will arrive.
British people not used to this sort of treatment might find Mustique hard to swallow. It's also rather expensive: the price for a room for two per night can rival the cost of your transatlantic flight. But you only need two or three days here, so intense is the experience. After lunch on the beach, full English tea is served in the main dining room. The room still has Colin Tennant's original decorations: armoires studded with cowrie shells are flanked by Indian chests and stuffed birds in glass cases. Every day at tea-time, triangular sandwiches arrive on trays, plus petits fours, banana bread and Caribbean tea with condensed milk.
Every Tuesday night the management of the Cotton House invites hotel guests and anyone else currently staying on the island, to a cocktail party. Unlike with most "drinks with the management" invitations, everyone turns up. Mustique is so small and the amusements on the island are so limited, that there's not much else to do. So you could end up having drinks with Mick Jagger, Spike Lee, David and Serena Linley, and Billy Joel, all at the same time. Then you get invited to pop back to their pads for dinner. It happens. "Don't take it too seriously," we are warned. "Casual, informal elegance. Wear your little black dress if you like, but with bare feet." Bare feet? For dancing on the beach. But don't forget to have a pedicure.
Rosie Millard paid pounds 300 for a London-Barbados ticket through Golden Lion Travel (01293 567800). The Treasure Beach in Barbados and the Cotton House in Mustique are both bookable in the UK through Unique Hotels (01453 835801). At Treasure Beach, the cheapest room until 12 April is pounds 278 without meals; from 13 April, the price halves to pounds 134. From now until mid-April, a deluxe room at the Cotton House costs pounds 370 half-board including tax. During the low season (16 April-15 December), the price falls to pounds 253.