In Florida, though, just off South Beach in Miami, lies Fisher Island, a lush, 216-acre enclave that, according to Census Bureau figures, is home to America’s richest community.

With its residents’ wealth averaging a cool $10m (£5.5m) and including the tennis star Boris Becker, entertainers Oprah Winfrey and Mel Brooks, as well as some of the biggest names in business (the former owners of Thomas Cook Travel and Blockbuster video, for example), the island has become one of the most valuable pieces of real estate in the Sunshine State.

The singer and actress Jennifer Lopez, according to American reporters, has shown interest in buying there, and the actor John Cusack has viewed homes to share with his Venezuelan girlfriend.

Not all its residents are American, however. In the past few years, an increasing number of Brits have forked out as much as £8.5m for a slice of Fisher Island, built in the 1920s as a winter escape by William and Rosamund Vanderbilt. While the island’s owners are reluctant to disclose any details about residents — even forbidding photography on the island — they admit that about a fifth of its 675 families are European, and “a good proportion of those” are British.

Karen Melk, whose husband, John, sold the island for a reported £140m in 2004 to British-based David Aim, 29, of Euro Fund Properties, says that since the takeover, the place has become much more European. “The new owner’s strategy has definitely been to try to inject some European style and glamour here,” she says, flashing a super-white, all-American smile as she shows me round her marbled penthouse home, looking over the sea towards the Miami skyline.

“We have Mediterranean restaurants, European designers in our boutiques, and are even giving our new projects European names: Palazzo del Sol, del Mare and del Luna.”

While the seaside condominium blocks bear no relation in reality to a true Italian palazzo, they have all the luxuries a European prince could ask for. The Melks’ apartment has marble floors, gilt wallpaper, wooden panelling, faux-antique furnishings, surround sound, plasma screens and the best kitchen equipment money can buy. Theirs is a relatively modest 4,000sq ft home, but some are up to 10,000sq ft.

Already, the 20 apartments in the newest development, Palazzo del Mare, priced at $1,000 (£560) per sq ft, are sold out (and a few are on the market already for resale at substantially higher prices). A four-bedroom, five-and-a-half- bathroom apartment, with 7,000sq ft of space, including a 1,340sq ft terrace overlooking South Beach, is on the market at £4m. A four-bedroom version spread over 3,700sq ft is for sale at £2.13m, and a smaller one in the same building has a price tag of £2m. The building has a full-time concierge service and private cabanas by the pool.

The vast size of many apartments reflects the fact that Fisher Island has become more child-friendly over the past few years. Melk shows me round the island’s private junior school, which now teaches 58 children under 10. “When Fisher Island first opened, it was really more of a place for CEOs to come and play golf and sail their boats in the winter,” she says. “Now it’s a family island, requiring family accommodation all year round.”

While it has a mile of white beaches (lined with fine sand imported from the Bahamas), free-form pools and a playground for children, most of the island’s toys are decidedly grown-up. Aboard the private ferry that transports residents or prearranged guests every 15 minutes to and from the island, limousines, Mercedes, Porsches and big, shiny black Bentleys decorate the decks. Yachts that make those in Monte Carlo look like toytown models line the docks. Golf carts (free with every residence) whizz about the manicured, palm-lined roads.

There are also plenty of added extras that come with being a part of what Phyllis Winick, Fisher Island’s president of real estate, calls: “the most unique, beautiful island in the world”. First, the club, which costs residents a cool £100,000 joining fee plus annual fees of £3,400-£5,600, the island’s eight beachside restaurants and bars, the 18-court tennis club, and the nine-hole PB Dye-designed golf course. There are monthly fees for maintenance of communal areas, such as hallways, garages and pools. Then there’s the spa, named by Town & Country magazine as one of the country’s top 10 (featuring a week-long detox for £6,000). And the marina, whose slips cost from £140,000. And, rather absurdly, in addition to state taxes, a local tax of about 2% of the property’s original purchase price to Miami City and South Beach, although the authorities provide only water and electricity (the roads, lighting, sewage and so on are all privately maintained by the island).

While to many people those figures sound absurd, they’re small change to the sort of residents the island wants to attract, Melk says. “When you’re attracting the cream of the world’s businesspeople, then really a couple of million isn’t a lot,” she says, dismissively. Winick is already predicting prices of $1,500 (£840) per sq ft for the next building to go up, before a stone has been laid, “and who knows what for the next?” she says. “We just can’t seem to put them up quickly enough.”

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