Forget yachts and jets, a private island is both a status symbol and a sound investment.

Seaside holidays are great, as any five-year-old will tell you. What’s not to like about sun, sand, pistachio ice cream and forkfuls of fried calamari?

The trouble is, there are more and more five-year-olds around. The beaches of Europe will be more crowded than ever this year, because alternative locations, notably Turkey, Tunisia and Egypt, have dropped off the bucket ‘n’ spade map due to the risk of terrorism.

There are, however, still places on both sides of the Atlantic where the coast is clear and you can enjoy splendid isolation, under slanting sun and symphonic clouds. They are the private islands on sale in the north of Europe, the Mediterranean, the Caribbean and the Indian Ocean.

Take Nissos Makri (above), in the centre of the Ionian Sea. It’s 993,900 sq m of Greek island heaven. You don’t have to take my word for it. The late Greek shipping billionaire Mr Aristotle Onassis liked the area so much he bought Skorpios, another island a short yacht ride away. It was there in 1968 that he married former US first lady, Ms Jacqueline Kennedy. Skorpios is now the property of Russian oligarch Mr Dmitry Rybolovlev. Another admirer of the islands in the Aegean and Ionian seas is the former Emir of Qatar, Sheikh Hamad bin Khalifa Al Thani – he has already snapped up six of them, including Oxia, for €8.5m, and is rumoured to be after 12 more.

You’ll always find a good spot on Nissos Makri’s 7km-long shore because you will be the only person there, if, that is, you have a few tens of millions of euros to spare. Nissos Makri is for sale. For a (small) fortune, you get to be de facto ruler of your own mini kingdom, and, if you want, you can develop it. There’s planning permission for a hotel and villas.

If tens of millions is a bit toppy for your budget, how about a price tag of £2m? (And falling by the day for overseas buyers, thanks to the slump in the value of pound sparked by Britain’s decision to vote to leave the EU.) It’s a small price to pay to become the laird of Tanera Mòr (above), the main island of the Summer Isles archipelago, 1.5 miles off the northwest coast of Scotland. The 310-hectare island comes with nine houses, including its own post office, plus a boathouse and slipways to make the short journey by dinghy to the mainland.

“A private island is the ultimate property investment and the market is very healthy right now,” says Mr Hugo Thistlethwayte, whose London firm, Savills, lists both islands.

Its robustness is due to the fact that both the number of potential buyers and the number of islands for sale are at record highs. Now that the republics that made up former Yugoslavia are peaceful, investors are dipping a toe into their waters. Islands in the archipelago that runs parallel to the Dalmatian coast, off Croatia, are the most popular. Currently on sale through specialist broker Vladi Private Islands is Bijela (below), 60,000sq m of olive- and pine-tree festooned land with a castle, an abandoned church and only 17km from Zadar airport by boat. The price is available on request.

“They have the advantage that they are very close to the main cities on the shoreline, notably Dubrovnik, Split and Rijeka,” says Mr Thistlethwayte.

Overall, more than 600 islands around the world have either come on the market for the first time in recent years or been put up for resale by their existing owner, analysts say. “There is more stock on the market and more people who not only can afford to buy but are happy to travel further to find what they want,” says Mr Thistlethwayte.

Even those with modest budgets have options. A simple internet search for reasonably priced private islands for sale produces a few surprises. There’s everything from Inishbigger, off the west coast of Ireland, for £60,000 ($80,000), which boasts five hectares of grazing land and – joy! – a peat bog, to an island off the coast of Sweden for £80,000 ($106,000), which comes with two houses.

Where’s a good spot for a first-time private buyer? Mr Thistlethwayte recommends the Caribbean, notably the British Virgin Islands or the Grenadines. “It’s the most stable market, has strong rule of law, the English language, good air links and airports, and it’s warm all year round, unlike the Mediterranean.”

Properties there are easy to rent, too. Mr Richard Branson’s Balinese-style home on Necker in the BVI is rented almost every day he and his family are not there. It’s yours for around £40,000 ($53,000) per night for up to 30 guests. (You do the maths.) The only downside is that the Caribbean can be pricey because it attracts buyers from Europe, the US and Latin America. “If you have your own plane and a good air strip, an island is weekendable from the US,” Mr Thistlethwayte explains. The Caribbean is a great place to party, too.

Also “weekendable” is the Bahamas, where you’ll find Big Sampson Cay (above). For $18m you can get 52 hectares of tapioca-white sand beaches, a natural harbour, three small beachfront cottages and a gravel strip suitable for a Cessna Caravan aircraft.

If you prefer doing sports to doing shots, the Maldives might be for you. Small atolls start from $5m. “Here, it’s more about nature, diving and fishing. There might be a bit of yoga, too,” says Mr Rod Taylor, who used to work for The Soneva Group – creators of the Maldives’ most loved barefoot luxury resort, Soneva Fushi – and now looks after Savills International development sales. It’s the same in the Seychelles, although the islands there take longer to get to because there are fewer airstrips, so you might need to take a boat ride or a helicopter.

Once you have worked out where you want to be, you have to navigate the choppy waters of buying. A few countries, notably the BVI and the Grenadines, offer freehold, but most islands are available only on a leasehold basis. Most are 50 years long. Extending them is a political negotiation with the government in each area.

After you’ve jumped through the diplomatic and financial hoops, the fun begins. And it’s the best kind of fun – fun on your terms. “If you own a private island, you have to bring your own fun. Anyone who is there is by your invitation and has to play by your rules,” says Mr Thistlethwayte. He pauses and adds: “If you want to walk around naked, you can walk around naked.” We don’t know about that, but owning your own offshore haven certainly helps put the “hip” in archipelago.