Local estate agents report selling two or three houses priced between £700,000 and £1.4m every month, but £3.3m is being asked for the Villa Stupalo, also in the Meje district of the town, which has a swimming pool, tennis court, gym and gardens.

Properties on some of the larger of Croatia’s 1,000 islands are also in demand. Ivica Vulic, of the Broker agency in Split, says that when his agency advertised a few islands on the internet, “there were a couple of very interesting offers from Hollywood”.

Stone houses on Hvar, one of the largest islands, just over an hour by ferry from Split, are going at roughly £800 per square metre.

But locals say the price can double if sellers find out the potential buyer is a westerner. “Interest is huge and that means the prices are going up step by step,” says Zoran Domancic, the mayor of the island’s capital.

Local estate agents say the demand has become so great, it is now outstripping supply. “There is more demand for old stone-built houses or villas in coastal areas than the Croatian market can offer,” says Ivica Murn, owner of the My Home estate agency in Crikvenica, northern Croatia.

But Brits who want to dive into the Croatian coastal- property market will have a head start on people from other European Union countries. Unlike many other EU states, Britain, along with Ireland, signed a reciprocal agreement on property purchases as part of a wider set of agreements before Croatia’s EU accession in 2007, which allows British and Irish nationals to buy property in Croatia and vice versa.

Under Croatian law, foreigners from countries who have not signed up to the reciprocal agreement — such as Austria — are not allowed to own property as private individuals in Croatia and can make a purchase only after setting up a company.

Murn, who says he has sold three properties to British and Irish clients in the past two months, suggests Brits may want to consider buying plots of land and then building a house.

“It is usually much cheaper,” he says. “The price of an apartment, for example, in coastal areas goes at between £800 and £1,400 per square metre. But on some more remote islands, you can still get land to build on for £70 per square metre.”

But he warned that there are few villas like Malkovich’s left: “There are some available in Opatija where the Austro-Hungarian emperors came for their holidays, but the demand is far bigger than any possible supply.”

Murn suggests instead investing in older stone-built estates or even small castles in need of repair: “You can get them for £30,000 — a damn good price for unique Mediterranean architecture.”

But he advises any potential purchasers to make contact with a reputable estate agent registered with the Croatian Chamber of Economy.

“I’m not trying to tout for business for my or any other estate agency, but by going to the Croatian Chamber of Economy you will avoid any problems that may come up in the future.”

Local laws on property sales and registrations are open to wide interpretation and subsequent legal claims could be problematic in courts where it is not uncommon for cases to take years to come to trial.

The property industry is less strictly regulated than in the UK. Sometimes agents are no more than people working under business licences allowing them the status of self-employed traders of unspecified goods or identifying them as “intermediaries” in business dealings.

Broker, 00 385 2 154 7004, www.broker.hr; My Home, 00 385 5 178 1575, www.agencija-myhome.com; Croatian Chamber of Economy, www.hgk.hr

Buying in the Balkans

Daksa Island is 500m from Dubrovnik and has a house (in need of repair) and a boathouse. Vianello Realty (www.vianellorealty.com) and www.privateislandsonline.com are selling it for £1.8m

This two-bedroom house is right beside the sea on Vis island, near Split. It has two terraces and mooring for a boat. Croestate (00 385 2 154 7004, www.croestate.com) is selling it for £50,000

In the town of Dugo Selo, about 30 miles from Zagreb, this house has four rooms plus a bathroom, and costs £37,000 through Real Estate Croatia (00 386 3 586 1665, www.realestatecroatia.com)

This stone house near Split is in need of renovation. Set in an Dalmatian village 500m from the sea, it is being sold by Real Estate Croatia (00 38 521 343 105, www.realestatecroatia.com) for £24,000

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