Theresa May and Jean-Claude Juncker
British Prime Minister Theresa May (L) shakes hands with European Commission chief Jean-Claude Juncker prior to a Brexit negotiation meeting on December 4, 2017 at the European Commission in Brussels JOHN THYS/AFP/Getty Images

Nationalist leaders from across the United Kingdom have voiced their concerns over a possible deal that could see Northern Ireland continue under EU trade laws and regulations.

In a bid to maintain the peace between Northern Ireland and the Republic, leaked reports have suggested that there would be no divergence in law across the island of Ireland, even after Brexit.

But leaders from the devolved regions have all raised concerns with the plans.

In Brussels, Theresa May was forced to exit talks without a signed deal.

Commission chief Jean-Claude Juncker said that there was no deal reached but that it was still possible by the end of the week.

He described May as a "tough negotiator" as the pair emerged after hours of discussions.

May admitted that "on a couple of issues, some differences do remain."

But both leaders were confident that an agreement could be met in time for the EU leaders summit on the 14 and 15 December.

Back in the UK, the possible Irish border deal has concerned leaders across the British Isles.

The most troublesome words have come from the leader of the DUP, Arlene Foster, who said that she would "not accept" any regulatory divergence between Northern Ireland and the rest of the UK.

Theresa May's minority government relies on the 10 DUP MPs, and Foster's disapproval could destabilise the talks.

"We must leave the EU on the same terms as the rest of the United Kingdom. The economic and constitutional integrity of the United Kingdom will not be compromised in any way," Foster said.

Meanwhile, in London, the mayor Sadiq Khan voiced similar concerns saying that there would be "huge ramifications for London if Theresa May has conceded that it's possible for part of the UK to remain within the single market & customs union after Brexit.

"Londoners overwhelmingly voted to remain in the EU and a similar deal here could protect tens of thousands of jobs."

Scottish First Minister Nicola Sturgeon was also unhappy with the possible deal.

She said: "If it's not some kind of Norway status for whole UK, it must mean some kind of special deal for NI. Has to be one or the other. And if latter, why not also for Scotland, London & Wales (if it wants it)?."