So how come it has become so favoured by the super-rich? Possibly because Anguilla's attractions fit the designer motto "less is more".
Less traffic, fewer crowds, fewer of the souvenir shops that spring up wherever big cruise ships come in. (After a brief experiment of allowing cruise passengers ashore, Anguilla banned them.) The outside world is not allowed to intrude.
Privacy is essential for the rich and famous now. So much so that at top-end estates like Temenos or Altamer (villa rentals reach $85,000 a week over Christmas) there's no guest book and the computer in the library is set up to rub out all record of previous occupants.
But privacy should not stop at the front gate (unless you're happy to spend your time in a gilded ghetto).
This is where tiny Anguilla's laid-back attitude kicks in. You can drop by the neighbourhood shack for some jerk ribs, or go jiving in rub-a-dub style at Johnno's down by Sandy Ground on a Friday night, or even join in a game of backgammon outside the general store — no matter how famous you are the locals won't bat an eyelid, let alone give you any hassle.
Nowadays, that kind of friendliness is a priceless commodity — especially when married to some of the most futuristic, whiter-than-white beachside properties to be found anywhere in the Caribbean. Take Altamer, for instance.
Designed by Myron Goldfinger,who also did the aerodynamically swept tower villas at Covecastles just around the bay, Altamer's purist combination of the cuboid and the spherical forms masks its real identity — which is to be the mother of all beachside party houses.
The sound system (which has "rock speakers" should you want to dance on the beach) is powerful enough to lay siege to any unco-operative Panamanian president.
The food is prepared by a Maxim's-trained French chef and served by butlers (plural) on a freestanding terrace reached by a skywalk so you can enjoy the moonlit seascapes with St Martin's rugged outline in the distance. Staying at Altamer — in the original
Russian-themed villa or its newer and even larger Brazilian and African-inspired neighbours — is indulgence to its illogical extreme.
Amazing architecture — Moorish-inspired, this time — combined with seamless service is the hallmark of the newly refurbished Cap Juluca.
This was the first of Anguilla's super-luxury hideaways, for which reason it sits upon what some judge to be the island's finest beach at Maunday's Bay.
Whether you stay in one of the villas with their own private pools or in the hotel suites, you can call on the services of three different restaurants and in-house masseuses or unwind with holistic body-and-mind sessions.
In between, that is, diving expeditions, floodlit tennis or dropping in on the private island of Scilly Cay for the freshest lobster and killer rum punches provided by Eudoxie and Sandra — nothing but first names here, Robert (De Niro) might be at the next table — while the local band pumps out some foot-tapping acoustic reggae.
Dining out on Anguilla is problematic — mainly because there is almost too much choice. For classic French and an award-winning wine cellar, there's the Malliouhana; for a delectable hint of south-east Asia and great views, Hibernia; for more homely American-Caribbean fusion, Blanchards.
And that's without mentioning the many local restaurants like E's Oven or Tasty's which do a refined version of jerk chicken or black bean soup. And where, unlike some other Caribbean islands, you feel genuinely welcome when you walk through the door..
DETAILS: ANGUILLA
THE FLIGHT BA flies from Gatwick to Antigua, £479 return, www.ba.com, then take a short LIAT flight to Anguilla, $156, www.liatairline.com.
THE HOTEL Cap Juluca has doubles from $525, www.capjuluca.com. ITC Classics has seven nights with flights from £2,200pp, www.itcclassics.com. Expedia has seven nights room only at the three-star Arawak Beach Inn for £964pp with flights, www.expedia.co.uk.
THE RESTAURANT Hibernia (www.hiberniarestaurant.com).