But nowadays Mustique is less of a real-life Celebrity Love Island and instead enjoys a sunny, if sedate, middle age.
Mustique was discovered in the 15th century but the island as we know it - where most villas cost £2m or far more, where every home has full-time staff and where villa rental can be over £1,000 a night - is less than 50 years old.
In 1958 it was bought from the government of the Grenadines - a cluster of small, beautiful Caribbean islands - by a wealthy Briton, Colin Tennant. Only 100 people lived there. In 1960 Tennant gave Princess Margaret a 10-acre plot as a wedding gift and her small house still stands today.
In 1968 Tennant opened the island up to well-heeled outsiders, mainly British. There were strict limits on how many homes would be built and existing residents would "interview" outsiders wanting to live there.
In 1969 the airport was opened and the first villas built under the direction of the theatrical designer Oliver Messel. Improvements followed - a small road network, reliable electricity, fresh water from a desalination plant, and then air services began to Barbados and other nearby islands.
Thirty-six years on, the island still has a post-war "Garden of England" look. Neatly manicured gardens are everywhere and the whirr of sprinklers is the only interruption to a blazing hot afternoon. There is no crime.
"Owners don't come here for a wild time so some kinds aren't attracted," says Brian Alexander, who since 1980 has headed the Mustique Company, which manages the island. He says the residents have rejected a few would-be owners "for financial or criminal reasons.
"People come here to relax. They have fabulous houses on the island with skilled staff and fresh local food so they don't go out. They probably spend the rest of their lives in restaurants and hotels anyway so this is a total break."
Mustique is so laid back it almost falls asleep as you look at it. Seven large, beautiful beaches provide scores of spots to snorkel, fish or swim. Otherwise, most entertainment is inside the gates of houses.
There are no gin-palaces in the harbour as islanders opposed expanding the port, which is used only to import food and for staff moving to and from other islands. The airport is tiny; again residents voted down a plan to extend it to be large enough for private jets.
There are only half a dozen shops and the drive-in cinema is a sheet strung between trees with a large grassy area for picnics. There are a handful of bars and restaurants, the most famous of which is Basil's, where Tommy Hilfiger is a regular. Otherwise the island is quiet and virtually dark after 9pm.
Because much of the island's population is at or near retirement age there is a steady turnover of homes. Those now on sale include Pelican Beach, a two-bedroom villa with grounds taking you within 50ft of the sea. It costs just under £2m. On sale at the same price is Endeavour Hills, a three-level villa above the sea with glorious views of most of the Grenadines. Nearby is the larger Blue Moon, a house with four en suite bedrooms overlooking the "sunset" side of the island. It comes with 3.5 acres, a vast pool and will set you back £4.7m.
Acceptance into the Mustique owners' club requires you to keep full-time staff - even the smallest villas have a gardener, cook and maid at least - but this can easily be recouped by letting out the property, especially during the winter high season.
Ownership also allows you to have a say in the future of the island, which is under review at the moment. Twenty-five more homes will soon be built, which is of concern to some residents; the 1,200 staff servicing the island use around 500 cars on roads designed 40 years ago for horses and the airport is so busy the Company wants residents to use scheduled services instead of private aircraft.
"The 21st century is creeping in but it's a case of managing it in an orderly way," explains Alexander. "The residents are intensely conservative so anything that changes must be gentle and with agreement. Nothing too disruptive can occur." As celebrity islands go, this is a quiet one. Abi Titmuss wouldn't want to live there. But you can tell without asking that the people of Mustique wouldn't allow her to, anyway.
All Mustique property is for sale via Knight Frank, 020 7629 8171.