Speaking in Belfast today, May said that while a border between the two will be inevitable, she was seeking a practical response to the new issues generated by the UK's vote to leave the EU.
56 per cent of Northern Ireland voted to Remain, while the Republic remains a member, and Sinn Fein have questioned whether the province should be removed from the EU against its will.
May met today with Northern Irish first minister Arlene Foster and deputy first minister Martin McGuinness today, and said talks had been both positive and constructive.
“If you look ahead, what is going to happen, when the UK leaves the European Union is that of course, here Northern Ireland will have a border with the Republic of Ireland, which will remain a member of the EU.
“But we’d had a common travel area between the UK and the Republic of Ireland for many years before either country was a member of the EU,” May said.
“Nobody wants to return to the borders of the past,” she added, referring to the province's history of security barriers, armed vehicle checkpoints, and permanent border posts manned by troops.
“What we do want to do is to find a way through this that is going to work and deliver a practical solution for everybody, as part of the work we’re doing to ensure that we make a success of the UK leaving the EU and that we come out of this with a deal in the interest of the whole of the UK.”
May will hold further talks on the implications of the Brexit vote for the island on Tuesday when she meets the Taoiseach, Enda Kenny, in London.