At odds over Brexit, leaders of Scotland, Northern Ireland and Wales meet Britain's PM May

British Prime Minister Theresa May (4th from left) chairing a meeting of the Joint Ministerial Committee, which is also attended by Scottish First Minister Nicola Sturgeon (6th from right) , Welsh First Minister Carwyn Jones (4th from right), and Nor
British Prime Minister Theresa May (4th from left) chairing a meeting of the Joint Ministerial Committee, which is also attended by Scottish First Minister Nicola Sturgeon (6th from right) , Welsh First Minister Carwyn Jones (4th from right), and Northern Irish First Minister Arlene Foster (2nd from right) and deputy First Minister of Northern Ireland, Martin McGuinness (far right) in London, Britain, on Oct 24, 2016. Discussions focus on issues around EU negotiations and the Economy.PHOTO: EUROPEAN PRESSPHOTO AGENCY

LONDON (Reuters) - The leaders of Scotland, Northern Ireland and Wales met British Prime Minister Theresa May on Monday (Oct 24) to discuss what part the three nations will play in the Brexit process, a thorny issue that risks triggering a constitutional crisis.

Mrs May proposes setting up a new committee to give the three devolved governments, which have varying degrees of autonomy from London, a formal avenue to express views on how Britain's future relationship with the European Union should work.

"The country is facing a negotiation of tremendous importance and it is imperative that the devolved administrations play their part in making it work," she said in a statement her office released before the meeting.

At stake is the three-century union between England, where a majority voted to leave the EU, and Scotland, where a majority voted to stay.

Scottish First Minister Nicola Sturgeon said on Monday she was seeking "meaningful input" into the decision-making structure and wants each of the United Kingdom's four assemblies to get a vote on the proposed negotiating package.

Ms Sturgeon has said her government is preparing for all possibilities, including independence from Britain, after Britain leaves the EU.

In Northern Ireland, which also voted to keep EU membership, there are fears that Brexit could undermine a 1998 peace deal and reinstate a hard border with the Republic of Ireland.

Experts have warned of the risk of a constitutional crisis if May does not take into account the position of each of the UK's four nations when conducting negotiations on the terms of Brexit.

"Imposing a Brexit settlement in the face of devolved opposition (while legally possible) would be a reckless strategy," said the Institute for Government, an independent think-tank.

"Scotland, Wales and Northern Ireland cannot be treated like any other lobby or interest group. Equally, the devolved governments will have to accept that Westminster will have the final say," it said in a report.

The new committee proposed by Mrs May would be chaired by Brexit Minister David Davis and include representatives from the three devolved governments. Mrs May proposes that it should meet by the end of November and at least once more before Christmas.

Ms Sturgeon has said Scotland wants to keep as many of the advantages of membership of the EU's single market as it can and is looking for a bespoke deal to do so.

The British government, however, has said it will negotiate a one-size-fits-all Brexit deal on behalf of the whole United Kingdom.

Mrs May's spokesman said on Monday that the UK needed a single nationwide position going into Brexit negotiations, and May expected the devolved governments not to undermine the overall Brexit talks by conducting their own negotiations.

Welsh First Minister Carwyn Jones said Wales, where a majority voted to leave the EU, wanted to play a full, positive and active part in the Brexit process and hoped the approach would be reciprocated by London.

"If UK Gov can't negotiate position with devolved nations little hope of negotiating a good Brexit deal with 27 countries," he said on Twitter.