Trawl through the specialist brokers’ websites, and you will catch islomania yourself. Got a spare £23.8m? Then why not snap up a matching pair in the US Virgin Islands? For sale with Private Islands Online, 510-acre Great Hans Lollik and 100-acre Little Hans Lollik in the Lesser Antilles chain have white sandy beaches and crystal-clear turquoise waters. They are zoned for low-density development and a single residential development respectively.

But islomaniacs don’t have to travel as far as the Caribbean for a bolt hole — or spend that much. St Athanasios is 2½ acres of Grecian hideaway in the Gulf of Corinth, 1½ miles from the city of Itea. It is being sold through Vladi Private Islands for £530,000, and is just crying out for a private villa to be built among its pine and olive groves.

There’s no need even to venture that far. The waters around Britain are dotted with islands, some of which occasionally become available.

In the Firth of Clyde, 684-acre Little Cumbrae Island has a ruined 13th-century keep and an elegant mansion with a garden designed by Gertrude Jekyll. Ten minutes’ boat ride from Largs, it is for sale through Coldwell Banker Morrison’s Private Islands for £2.5m.

The 45-acre Green Island, one of five isles in Poole Harbour in Dorset, was sold last year for £2.5m. At around the same time, Stack Rock Fort, a 19th- century fortress on a small island in Milford Haven, Pembrokeshire, was put on the market. Despite its lack of basic amenities — no water, no power and no sewerage system — it was snapped up within weeks by a local buyer, who paid the £150,000 asking price. “We don’t think he has done anything with it yet,” says Haynes Agency, which handled the sale. “It’s very dangerous to get on to — the steps are all gone.”

Safety is just one of the points potential buyers need to think about. “You have to consider not only the price of the island but how much it will cost to bring it up to liveable standards,” advises Morrison. “Is there fresh water? Is a home included? If not, construction costs will be about 30% or more than for mainland homes. How do you go back and forth? Can you live comfortably in isolation with no stores or restaurants within walking — or swimming — distance?”

Access was one of the problems faced by Deborah Clark, 44, and her husband, Tony Orchard, 56, who paid just over £2m for Burgh Island, off the Devon coast, after getting married there in 2001. “We’re at the meeting point of two tides,” says Clark, “and twice a day there’s no access by boat.”

The solution is a unique 1960s sea tractor, lovingly restored — like the Grade II-listed art-deco hotel on which the couple have spent a further £2m — and their own home, a house in which Agatha Christie is reputed to have written. Their sons, Theo, 9, and Lucas, 7, take the sea tractor to school in the morning — without enthusiasm, says Clark. “It’s not ‘Goody goody!’ It’s, ‘Oh no!’” Life on Burgh Island is very different from the family’s previous existence: Clark was a partner in a City law firm and Orchard a freelance property consultant. The hotel employs about 40 staff, half of whom live on the island, and all supplies arrive over the beach.

Take into account rivers, lakes and fjords as well as oceans, and countless islands are ripe for Blue Lagoon moments or Famous Five- style adventures. Size, climate, supply and demand all play a part in determining the price of islands.

Redmond advises that bargain hunters would do well to consider Canada.

Finland claims to have more islands than any other country, with a stated total of 179,584; however, Canada probably has more, with 2m lakes and thousands of miles of rocky coastline.

Canadian examples offered by Private Islands Online include two in Nova Scotia: Sheep Island, an 18-acre wooded isle for £59,000, and one-acre Davis Island for about £13,200. Vladi Private Islands, which has an office in Halifax, Nova Scotia, has about 40 Canadian islands on its books.

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