By Amanda Ferguson

BELFAST (Reuters) - Britain does not want a return to border controls in Northern Ireland, Prime Minister Theresa May said on Monday on her first visit to the British province following the United Kingdom's vote to leave the European Union.

The June 23 Brexit vote has raised a number of questions for Northern Ireland, from its impact on 18 years of peace, to billions of pounds of EU funding and the open border with the Irish Republic, which will be Britain's only land frontier with the bloc.

"We had a common travel area between the United Kingdom and the Republic of Ireland many years before either country was a member of the European Union. Nobody wants to return to the borders of the past," May said, referring to the freedom of movement that has existed between the countries since the 1920s.

"What we do want to do is to find a way through this that is going to work, deliver a practical solution for everybody to ensure that we come out of this with a deal which is in the best interests of the whole of the United Kingdom."

Northern Ireland voted to stay in the EU, with 56 percent voting 'Remain', putting it at odds with the United Kingdom's 52-48 percent result in favor of leaving.

The border issue has arisen because those in favor of leaving the EU were adamant that Britain must be able to control its borders - and hence immigration - more closely. Any new arrangements must also be agreed by all EU member states.

May was speaking after she met the province's leader, Arlene Foster, who campaigned for Britain to leave the EU, and Deputy First Minister Martin McGuinness, a former Irish Republican Army commander who campaigned to remain.

FRANK EXCHANGE

McGuinness, who has demanded a referendum to split Northern Ireland from the United Kingdom so it can remain in the European Union as part of a united Ireland, said he had a frank exchange with May emphasizing the wishes of the Northern Irish voters.

"I speak for the people of the North, who are Unionist and Nationalist, and have made it clear that they see their future in Europe ... There is no good news whatsoever in Brexit for anybody in the North," said McGuinness, who also raised concerns about the future of projects that are funded by the EU.

Leaders south of the border have been seeking support across the EU to preserve freedom of movement and goods across the island but acknowledged that controls at Northern Irish ports and airports may be required.

Foster, who is the leader of Northern Ireland's largest pro-British party, said she told May that there must be no internal borders within the United Kingdom and that the Prime Minister had responded positively to that.

Concerns have also been raised about the legal status of the 1998 Good Friday Agreement, which ended three decades of fighting between Catholic nationalists seeking a united Ireland and Protestant unionists who wanted to keep Northern Ireland British. Over 3,600 died in the conflict.

On Monday, a coalition of Northern Ireland politicians and human rights activists threatened a legal challenge against any British government move to leave the European Union unless the province's peace process is protected.

The group, which includes members of the province's two largest Irish nationalist parties said they would apply for a judicial review if moves to exit failed to safeguard the Good Friday Agreement peace accord.

The accord, which gives the Republic of Ireland a role, contains several references to the EU.

(Reporting by Amanda Ferguson; writing by William James and Conor Humphries; editing by Guy Faulconbridge and Giles Elgood)