Fancy a trip to my island?” As chat-up lines go, it has the edge on “Let’s go back to my maisonette.” Not only does a private island allow you to get away from it all — motorway tailbacks, Asbo neighbours, speculation about Tony Blair’s leaving bash — but by owning one, you join the ranks of celebrity island owners such as Johnny Depp, Claudia Schiffer, Sir Richard Branson and Edward de Bono.

Doesn’t sound like you? Don’t be put off by the big names, insist the experts: they are just the glitzy tip of a substantial iceberg. “Owning an island has always implied membership of an exclusive club,” says Renée Redmond, director of operations at Private Islands Online. “But most people don’t realise that owning a private island is affordable for the average person.”

Indeed, with the average price of a house in London now more than £300,000, many isles with five-figure price tags look more attractive than ever.

“Last year, I sold three islands in the Philippines to an American for less than $100,000 [£53,000],” says Cheyenne Morrison, island broker at Coldwell Banker Morrison’s Private Islands, a firm based in Australia. “He’s a restaurant critic, which isn’t a lucrative job.”

Private Islands Online and Coldwell Banker Morrison’s are two of the three firms that dominate the private island- sales business; the other is Vladi Private Islands. All three offer copious advice to the prospective buyer, and are run by characters who seem a race apart from ordinary landlubber estate agents.

Morrison admits to a “medical condition” called “islomania”, a term made famous by the writer Lawrence Durrell. “I know of no greater joy in life than to get my first sight, in the half-light of an early dawn, of an island looming off the bow of a boat,” says Morrison.

Farhad Vladi, of Vladi Private Islands, who grew up in Germany reading and re-reading Robinson Crusoe, has sold more than 1,500 islands. When discussing his favourite subject, he can sound like Swiss Toni, The Fast Show’s car dealer.

“To buy an island,” says Vladi, “is the same as courting a woman. You can never explain exactly why you love her. It’s chemistry — something you cannot define ” It’s why, in the mid-1990s, Depp fantasised out loud about following the example of the late Marlon Brando — who bought a Tahitian island hideaway 30 years ago — and then ended up paying nearly £2m for 45-acre Little Hall’s Pond Cay in the Bahamas.

It’s why his fellow A-lister Mel Gibson reportedly paid £7.8m for his Fijian island retreat, and it is certainly why James Martin, the British author of The Wired Society, and one of the world’s most respected futurologists, spent more than £5.25m building a dramatic new home amid the ruins of a 19th-century fort on a seven-acre island in Bermuda. Douglas Hedley-Coates, the architect who supervised its construction, wouldn’t say what the island cost Martin, but local property sources say it was sold for about £1.85m.

Gunpowder Island is so close to the channel into Hamilton Harbour that the draught from passing cruise ships sucks water off some of its beaches and sends it crashing back in a “mini-tidal wave,” says Hedley-Coates.

Yet the moment Martin first stepped ashore in April 1997, he was enchanted. “I have two strong feelings whenever I go to the island,” he says. “A sense of adventure and a sense of being in a remarkably beautiful and more peaceful world, a world far from stress.”

Hedley-Coates transformed the island’s quarries into ponds. A 19th-century latrine became an orchid house. A formal garden was installed on the roof of the old gunpowder magazine. The pumping engines of an aquarium, destroyed in a hurricane in 1922, were recovered and turned into ornamental features.

Martin, 73, divides his time between a mountaintop estate in Vermont, a home in South Africa, and his island. He has planned for both the building and the landscaping to survive long after his death. “It is for our children, their children and their children,” he says.

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