Theresa May. Philip Toscano/PA Wire

The first minister said Mrs May’s appointment, in a much shorter timeframe than previously thought, will help “reduce some of the political uncertainty” across the UK.

Mrs Foster also paid tribute to David Cameron as he prepares to leave office – “particularly for the role he played in Northern Ireland on issues from the devolution of corporation tax to assisting with PMS savers and of course his role in the political process”.

The DUP leader said: “I wish Theresa May every success as she becomes prime minister of the United Kingdom and assure her that we stand ready to work with her in the best interests of Northern Ireland and the United Kingdom.”

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Mrs Foster said: “It is important that she can commence work on planning the UK exit and the new arrangements to be negotiated.

“My colleague Nigel Dodds has already had discussions with Oliver Letwin MP about Northern Ireland’s place during the negotiations and I look forward to early discussions with our new prime minister when she takes up her post.”

Mrs Foster added: “We will be emphasising the unique circumstances that Northern Ireland faces and the need for regional administrations to work in partnership with the national government to bring about tailored solutions. The Northern Ireland Executive will continue its work planning for the various scenarios and I will be leading that work over the summer.”

The two Ulster Unionist MPs have also welcomed an early resolution to the Conservative leadership contest.

Danny Kinahan said: “I believe that, as prime minister, Theresa May will provide the much needed steady hand that the United Kingdom requires at this point in time.

“In terms of Northern Ireland, I hope that she will listen to those of us who cherish and value the Union and work with those of us who want to see proper democracy in action at Stormont, with a fully functioning Executive and Opposition.”