By Tatiana Jancarikova

BRATISLAVA (Reuters) - Britain wants a bespoke model for its future ties with the European Union, Prime Minister Theresa May said on Thursday, adding that its exit deal must address British voters' concerns over immigration.

Speaking after a meeting with Slovak Prime Minister Robert Fico in Bratislava - the latest in a flurry of diplomatic visits following Britain's June 23 decision to leave the EU - May stressed the need to have an open mind about what deal could be struck on the key issues of free movement and trade.

"We should be driven by what is in the best interests of the UK and what is going to work for the European Union, not by the models that already exist," she told a news conference.

"We need to find a solution that addresses the concerns of the British people about free movement while getting the best possible deal on trade in goods and services," May said.

In searching to solve the riddle of how to restrict EU migrants' freedom to live and work in Britain but retain access to the EU's single market for goods and services, politicians have picked over how other outsiders interact with the bloc.

Britain could try to join the European Economic Area or European Free Trade Association, forging a close partnership similar to those that Norway, Switzerland or Iceland have with the EU.

While that might please the EU, May would have to persuade Brexit voters to agree to the EU budget contributions and migrants that are accepted by some of those countries.

Crucially it would also lack the kind of EU market access for services which is so important to Britain's big financial sector.

OPPORTUNITY TO REFLECT

Slovakia holds the presidency of the EU Council, made up of leaders of all 28 member states, until the end of the year. That gives the country an enlarged role in responding to the initial shock of Britain's vote to leave that has thrown up questions about the bloc's future.

Fico said the European Union seemed to be falling in love with itself and needed to use the time before Britain formally starts divorce proceedings to create a new vision of Europe.

"This is an opportunity for both sides to reimagine and redesign a new project of mutual relations, a project that will be equally attractive both to the citizens of the United Kingdom and the European Union," Fico said.

Seeking time to prepare its negotiating stance, May said Britain would not trigger the formal Article 50 exit process before the end of the year.

Fico said the intervening period should be used to reflect not only upon Britain's future ties, but for the rest of the bloc to reassess its global position.

"I have always said ... the EU seems to be falling in love with itself," he said. "We wanted to be the best in the world. But it seems many regions in the world are far ahead of us. Let's use Brexit as a good occasion to reevaluate this."

(Additional reporting by Michael Holden; writing by William James; editing by Guy Faulconbridge and Giles Elgood)