Seated in front of a perfectly grilled fish in a seafront restaurant on the Croatian island of Brac, it is difficult to imagine that a decade ago, the country had just emerged from the bloodiest conflict to have been waged on European soil since the second world war. Small groups of tourists wander along the cobbled waterfront of the little port of Bol; boats bob gently in the harbour as the waiter brings more white wine.

A welcome air of normality has, at last, descended over the Balkans. After a false start, Croatia is on its way towards membership of the European Union, while its old foe, Serbia, if not yet welcomed entirely into the fold of democratic countries, has just been granted the ultimate accolade for a civilised nation: victory in the Eurovision Song Contest.

It is not just the tourists who have returned to the Dalmatian islands, even if numbers still lag behind those in the 1970s and 1980s, when what was then Yugoslavia was a popular package-tour destination. British property-buyers are coming, too, encouraged by the recent introduction of low-cost flights to Zadar and Split, which have brought most islands within easy reach of home.

Don’t expect rows of horrible high-rises – or bargain-basement prices, for that matter. Although the islands have their share of new houses and flats, Croatia has tough planning rules that restrict building, especially close to the shore. Think Greek islands or parts of the Côte d’Azur, rather than the brash Bulgarian Black Sea resorts marketed so relentlessly to British buyers.

“There are new developments, but they tend to be sympathetic to the environment, especially on the islands,” says Christen Thomson, a senior manager with the agents Colliers International, who covers southeast Europe from the Croatian capital, Zagreb. “The authorities are extremely rigorous about how new places should be constructed, down to the precise stones or tiles used.”

So, where should you buy in a country with more than 1,100 islands? True, only 50 or so are inhabited, but it still makes for a bewildering choice. Probably the most attractive are the southernmost clutch between Split, served by EasyJet, from Gatwick, and Wizzair, from Luton; and Dubrovnik, to which you can fly with British Airways, from Gatwick, and several charter companies.

A good starting point is Brac, which, at 153 square miles, is the largest of the southern Dalmatian islands and an hour’s ferry ride from Split. Ljiljana Poklepovic, who runs Milenka Real Estate, an agency based on the island, says that British buyers began arriving in large numbers two or three years ago, joining the French, Italians and Germans who were already there. While Bol, in the south, remains popular – thanks, in large part, to nearby Zlatni Rat (the golden cape), probably the best beach in Croatia – many Britons make for Milna and Bobovisca, in the west.

“English people are not like other people,” says Poklepovic, with refreshing candour. “They don’t want to spend much money, but they do want something they can renovate and be creative with.” Most popular are old houses with a garden in a good location. Despite consistent price rises of at least 20%-30% over the past few years, it is still possible to buy a 1,600 sq ft property with some land for £135,000; renovated, the same property could fetch more than £240,000.

Frederick Abernethy, 61, a company director from Saltford, near Bath, and his wife, Isobel, 60, chose the island of Hvar, just to the south of Brac, buying a three-bedroom flat in Hvar town two years ago. “We felt like pioneers,” says Isobel. “At the time, nobody was even going to Croatia. When we got back, people asked us if the war was still going on.”

The couple initially considered buying in Montenegro, but were drawn to Hvar by its quiet charm. “We saw it and fell in love; it was very much the old Croatia,” she says. “The people were lovely, and we didn’t feel as if we were being ripped off all the time. It is so refreshing that there aren’t English pubs or places offering English tea all over the place.” The island is changing fast, however: its reputation as a chic holiday destination has been enhanced by sightings of Princess Caroline of Monaco, Giorgio Armani and Bernie Ecclestone, whose wife, Slavica, is Croatian.

Things are a little quieter in Korcula, the next island down from Brac, whose main claim to fame is that it was the birthplace of Marco Polo. Yet, thanks to its quaint fishing villages and dense forests, the scenery is just as beautiful.

Those really looking to get away from it all should make for tiny Vis, further to the southwest. At one stage, during the second world war, it was the main hideout of Josip Broz Tito, the future Yugoslav president. The Scottish diplomat, soldier and adventurer Fitzroy Maclean, who was Churchill’s envoy, helped to turn it into the last bastion against the Nazi occupiers.

Vis was closed to tourism by the Yugoslav army at the end of the war and reopened only after Croatia declared its independence in 1991. It has since acquired an arty, bohemian feel, but is not as easy to reach as the other islands. The ferry from Split takes three hours and runs infrequently out of the summer season.

If ease of access is important, then Peljesac is worth considering. Connected to the mainland by a narrow stretch of land, it is a peninsula rather than an island, but shares much of the topography and charm of Brac and Hvar. It was this chance to have the best of both worlds that attracted Matthew Richard-son, 37, from West Sussex, who runs a computer-services company, and his wife, Kerry, 34. In 2004, the couple bought a former sea captain’s house in a hamlet of 15 houses above the seaside village of Viganj, near the tip of the peninsula.

“I say a house, but what we were buying was the location, a footprint and four walls – they are 90cm thick, made of solid local Korcula limestone, and have been standing since the 1750s,” Matthew says. The Richardsons, who bought with another British couple, paid about £100,000 for the house and spent £85,000 to have local craftsmen turn it into a beautifully reconstructed four-bedroom home that they call The Captain’s House.

“All the properties were destroyed by a forest fire, but have been bought by foreigners, British and Germans, and are being restored,” he says. “One of the main attractions of buying here was that we couldn’t see the possibility of any significant developments. We felt the area would remain unspoilt, or at least be spoilt later than elsewhere.”

Prices on all the islands are certainly rising, but similar properties can be offered for very different amounts. Vendors often decide how much to charge according to how much money they need, rather than any objective measure of what their property is worth.

Wherever you buy, brace yourself for plenty of complications, and make sure you have good legal advice. First and foremost, ensure that the seller actually owns the property – 100% of it, that is. The Croats have been bad at handling their land registry over the years, and old properties may turn out to be part owned by many relatives, some of whom will have long since emigrated to Australia or America. The last thing you want after completing a painstaking and expensive renovation of an old stone farmhouse is for a long-lost cousin from Sydney to pitch up and demand his share.

The buying process, too, can be complicated. Foreigners do not have an automatic right to buy, but must obtain authorisation from the justice ministry. This is effectively automatic, but can take months: in the meantime, although you are able to occupy your property, it will not be entered in the land registry, which can cause problems. The alternative is to set up a Croatian company and buy through that. The process is simple, and should cost no more than £1,500, but the running costs can begin to build up.

A hassle? Maybe, but it might be worth it, not just for the view, but for that perfectly grilled fish.