“Caribbean?” asks Farhan Vladi, the world’s leading island-broker, “or Pacific?”

The demand for private islands has never been higher. During the Cold War the rich would build nuclear shelters on their estates. Now they are looking for a piece of land surrounded by sea where they can support themselves when Armageddon arrives.

“It’s the fear of terrorism,” says Mr Vladi, who sold his first island in 1970 at the age of 25, “coupled with the fear that quality of life is disappearing. The two anxieties are linked.”

Since September 11, 2001, Hollywood stars have been piling into the island market.

Johnny Depp bought the 45-acre (18 hectare) Little Hall’s Pond Cay in the Bahamas, with its six private beaches. Leonardo DiCaprio snapped up a 104-acre island with an airstrip in Belize.

Nicolas Cage and Mel Gibson have also secured their bolt holes. There is romance involved too, of course, and the burning desire to escape briefly from the paparazzi.

Businessmen out of the media spotlight have also been gripped by the buying frenzy. Leonardo Ferragamo, of the Italian shoe dynasty, is also owner of an island, as is Bernard Arnault, who owns 50 per cent of Louis Vuitton Moët Hennessy.

In the days of the ship owner Aristotle Onassis islands were little more than fashion accessories for the super-rich. Now, Mr Vladi says, they have become an important cog in a new survivalist mentality. There is a run on islands in Canada and New Zealand, countries that are thought unlikely to be drawn into some apocalyptic war between Islam and the West.

The sales numbers are unclear — deliberately so, since most owners insist on discretion — but several dozen have exchanged hands since 9/11. The New Zealand inventory lists 21 islands and island properties — 11 have been sold recently or are under offer.

“What is the worst thing that can happen?” says Mr Vladi, who has sold 1,800 islands in his career. “A terror attack on a nuclear power station is my bet. So you want an island where the winds are in your favour. In New Zealand the winds come from the South Pole, which is perfect.”

Mr Vladi has bought his own island there and a proud photograph of his 50 cashmere goats is propped up close to his daughter’s graduation picture. “I find I can work six weeks there over Christmas because new technology keeps me in touch.”

And that is the point: islands used to be the preserve of those who favoured exclusive getaway holidays. Now, as survivalist options, they have to be both remote (well away from radioactive clouds) and in touch.

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