LONDON – Britain wants to find a “practical solution’’ to ensure there will be no new border controls between Northern Ireland and the Republic of Ireland when the UK leaves the European Union, Prime Minister Theresa May said on July 25 in Belfast.

Northern Ireland is the only part of the United Kingdom to share a land border with another EU member. Residents and businesses on both sides of the frontier fear a return to customs and immigration controls along the unmarked border.

The UK and Ireland had shared a common travel area since “many years before either country was a member of the European Union. “Nobody wants to return to the borders of the past,’’ May said after talks with Northern Ireland First Minister Arlene Foster and Deputy First Minister Martin McGuinness that focused on the potential consequences of a British EU exit.

The referendum result also raises questions about the future of Northern Ireland, which experienced decades of violence between Irish nationalists and British unionists that have eased following a 1998 peace settlement.

The leaders of Northern Ireland’s power-sharing administration took opposite sides during the referendum campaign. Foster’s Democratic Unionist Party backed the “leave’’ side, while McGuinness’s Irish nationalist Sinn Fein campaigned to “remain,’’ arguing that a British exit would force authorities to revive trade barriers and renew physical security measures on hundreds of cross-border roads.