You would then have had have to explain you were talking about a 1,400-acre outcrop of rock in the Caribbean, populated by some 100 souls and their livestock, devoid of roads, jetty or any other infrastructure.
Then, in 1958, the island – part of the Caribbean archipelago of St Vincent and the Grenadines – was bought by the young Scots brewing heir Colin Tennant, Lord Glenconner. Under his visionary ownership it would evolve into an exclusive resort, playground of the rich, the famous and the royal, renowned for its celebrity partying – not to mention the odd royal scandal.
Five decades on and 40 years this week since Tennant established the Mustique Company, the presence of Prince William – fresh from his month-long naval posting in the Caribbean – and his girlfriend Kate Middleton, carries on the island's tradition as a royal retreat. Current property-owners on the island, such as rockers Sir Mick Jagger and Bryan Adams, fashion designer Tommy Hilfiger and entrepreneur Felix Dennis, maintain the celebrity cachet, while other high-profile celebrity visitors have included Hugh Grant and Jemima Khan and Zoe Ball and her husband Norman "Fatboy Slim" Cook.
Little visited by the wider world, the island still has some vestigial shadows of its past. Its abandoned Endeavor sugar mill and Cotton House are relics of long-vanished plantation days.
Mustique seemed an unlikely purchase for the restless young baronet, who paid a mere 45,000 for the island. He immediately began developing it and, in 1960, secured its status as a celebrity hideout by presenting Princess Margaret – for whom his wife was a lady-in-waiting – with a ten-acre plot of land there as a wedding present. Mustique became the Princess's holiday spot; though it has to be said that her new husband, Lord Snowdon, didn't share her enthusiasm for the place, referring to it disdainfully as "Mustake".
Maybe it was a premonition, as during the declining years of their marriage the Princess frequently holidayed there, holding court at her villa, Les Jolies Eaux. Despite seeking privacy, she was famously photo-graphed there, swimsuited, with her much younger lover Roddy Llewellyn. Margaret maintained her retreat there for 30 years, eventually suffering her first stroke while visiting the island in 1998. (She died in 2002.)
The Princess's presence established Mustique as an ultra-exclusive resort, with non blue-blooded celebs such as Mick Jagger, Bryan Ferry and David Bowie also taking to the island life.
In August 1968, Glenconner – who inevitably cut a picturesque, exotically clad figure – established the Mustique Company, entering into an agreement with the government of St Vincent and the Grenadines which effectively leased the island to the company. Their aim was to develop it for upmarket tourism while safeguarding its character.
Glenconner improved amenities for the locals, oversaw the planting of coconut palms and fruit groves and the creation of an airport. He brought in designers such as Oliver Messel and architect Arne Hasselquist and multimillion-pound villas began to emerge.
The island was draining his family fortune, however, and in 1977 Glenconner sold the majority of shares in the Mustique Company to a consortium headed by a Venezuelan, Hans Neumann, who owned a villa on the island. In 1988 Mustique was sold to 55 shareholders and villa-owners, and is still run now as a consortium of landowners.
Asked how much the island has changed over the past 50 years, Brian Alexander, who was its managing director for the past 29 years until retiring in April, replies simply: "From nothing to what it is today.
Glenconner purchased it from a St Vincent family called Hazell. "His family had an estate in Tobago which wasn't producing and his father sent him out to sell it," explains Alexander. "So he sold it and, on a schooner coming through the islands came upon Mustique. He telegraphed his father asking for permission to buy it. His father said, 'As long as there's water Colin, go ahead.' There wasn't, but he bought it anyway."
Today, with its population reaching 1,500 during peak season, the island boasts 100 privately owned villas, 65 of which are available for weekly rental, ranging from $4,250 to $150,000, as well as housing for 1,000-plus Mustiquean employees and the island's fishermen.
Glenconner, whose family home remains The Glen, a stately pile in the Borders near Innerleithen, now spends most of his time on St Lucia, where for many years he ran the Bang Between the Pitons restaurant.
A television documentary made in 2000, The Man Who Bought Mustique showed him in a less-than-flattering light: a boss clearly used to having his own way and referring to those running the island now as "smug, small-minded people, mostly rather inept" and the local workers as "slow and stupid".
Mustique still boasts only one hotel, the Cotton House, no traffic lights and the famous Basil's Bar – home to the Mustique Blues Festival which, while raising funds to provide schooling for local children, remains surely an incongruous pairing of the music of the disenfranchised with the jet set who can afford to holiday in one of the most exclusive resorts in the world.
For further details, visit the web at www.mustique-island.com