Update: Brexit deal must be done on a UK-wide basis, says Scottish Conservative leader

Her comments come as Scotland's First Minister Nicola Sturgeon urged politicians from all parties to get behind a deal to keep the whole of the UK in the European single market.

Crunch talks with the European Union (EU) ended without agreement after the DUP - which props up the minority Conservative Government in Westminster - made clear it would not accept any arrangement which saw the North treated differently from the rest of the UK.

It is understood the UK Government and the EU had been poised to agree to guaranteeing ''regulatory alignment'' between the North and Ireland in order to prevent the imposition of a hard border.

Leaders of devolved administrations - including Ms Sturgeon - made it clear any special status for the North would prompt demands from other parts of the UK for their own tailor-made Brexit.

Ms Davidson said: "The question on the Brexit ballot paper asked voters whether the UK should stay or leave the European Union - it did not ask if the country should be divided by different deals for different home nations.

"While I recognise the complexity of the current negotiations, no government of the Conservative and Unionist Party should countenance any deal that compromises the political, economic or constitutional integrity of the United Kingdom.

"All sides agree there should be no return to the borders of the past between Northern Ireland and the Republic of Ireland.

"Similarly, jeopardising the UK's own internal market is in no-one's interest.

"If regulatory alignment in a number of specific areas is the requirement for a frictionless border, then the Prime Minister should conclude this must be on a UK-wide basis."

Ms Sturgeon said that if one part of the UK can retain regulatory alignment with the EU and effectively stay in the single market, there is "surely no good practical reason why others can't".

She said there was now an opportunity to push for a Brexit deal that could keep the whole of the UK in the single market and customs union, and challenged others to back such a position.

She tweeted: "This could be the moment for opposition and soft Brexit/remain Tories to force a different, less damaging approach - keep the UK in the single market and customs union. But it needs Labour to get its act together. How about it @jeremycorbyn?"

This could be the moment for opposition and soft Brexit/remain Tories to force a different, less damaging approach - keep the UK in the single market and customs union. But it needs Labour to get its act together. How about it @jeremycorbyn?

— Nicola Sturgeon (@NicolaSturgeon) December 5, 2017

Earlier: May in race against the clock to break Brexit talks deadlock

Theresa May is engaged in a race against the clock to find the key to break deadlock in Brexit talks.

The UK Prime Minister's hopes of securing agreement on the terms of Britain's EU withdrawal were dashed on Monday when the Democratic Unionist Party refused to accept proposals which would have shifted Northern Ireland's customs border to the Irish Sea.

Mrs May is planning to return to Brussels before the end of the week, with time running out to persuade leaders of the remaining 27 EU nations at a summit on December 14-15 that "sufficient progress" has been made on divorce issues to move Brexit negotiations on to their second phase.

This will deal with trade and the transition to a new relationship.

Today, she was expected to speak by phone with DUP leader Arlene Foster as she grapples to find a form of words acceptable to the Northern Irish party, on which she relies to prop up her minority administration at Westminster.

Mrs May had to break off from talks with European Commission president Jean-Claude Juncker on Monday for an urgent call with the DUP leader, after she dramatically declared her party's implacable opposition to proposals which would have imposed "regulatory alignment" between Northern Ireland and the Republic in order to avoid the need for a hard border.

Taoiseach Leo Varadkar said that the deal had been agreed by the European Commission, UK and the Republic before the process was thrown into disarray by Mrs Foster's eleventh-hour intervention.

He said he was "surprised and disappointed" by Mrs May's request for more time.

European Council president Donald Tusk confirmed that, until the surprise developments at Stormont, he had been preparing to issue new negotiating guidelines for the second phase of talks today.

It is also understood that differences also remain between the EU and Britain over the issue of European Court of Justice jurisdiction over EU nationals living in the UK after Brexit.

Mrs May insisted she was still "confident" of getting a green light for trade talks at next week's summit.

Failure to do so would risk throwing the whole Brexit process into crisis, as many companies are believed to be preparing to activate contingency plans to start moving staff and activities out of the UK if there are no signs of progress by Christmas.

EU officials are understood to believe that a text of the deal must be thrashed out by the end of the week to allow it to be included in draft summit conclusions and give other leaders time to consult their own governments - and in some cases parliaments - before convening in Brussels.

Prominent Tory MPs voiced their opposition to any deal which threatened the territorial integrity of the United Kingdom by forcing Northern Ireland to operate under different regulations from the mainland.

Leading Brexiteer Jacob Rees-Mogg said: "I don't think that can possibly happen. The government doesn't have a majority for that."

Leaders of devolved administrations in Scotland, Wales and London said that they would want the option to adopt in their parts of the UK any special status afforded to Northern Ireland.

UK Labour leader Jeremy Corbyn said the failure of talks showed Mrs May's Government was "completely ill-equipped to negotiate a successful Brexit deal for our country", while former Ukip leader Nigel Farage said she should "leave office now".

But many Conservatives were optimistic of a deal being struck.

The chairman of the Commons Northern Ireland Committee, Tory MP Andrew Murrison, told BBC2's Newsnight: "We understand that later this week there is every prospect of a deal satisfying the European Union that, in its words, sufficient progress has been made which will set us up for a favourable conclusion to the summit.

"The mood here at Westminster at the moment is far more upbeat than I've known it for some considerable time now. I think, with compromise on both sides ... we are set fair for some good news before Christmas."

Minister for Agriculture Michael Creed told Newsnight that "with goodwill on all sides" a deal could be agreed by Friday, but added: "I don't want to underestimate the significance of the issues that have yet to be agreed."

Former top UK Foreign Office official Lord Ricketts said the row was "damaging" for Mrs May and will leave EU leaders with the impression that she lacks the authority to get through Brexit negotiations.

He told BBC Radio 4's Today programme: "I mean, it's pretty extraordinary that this wasn't all stitched up with the DUP beforehand.

"We're used to prime ministers going to Brussels and having a row with the EU and coming back without an agreement, but to go agree with the EU and then have a row on your own side is inconvenient."

He went on: "It leaves an impression, I think, in Brussels that the Prime Minister hasn't got authority over her own side and that will knock confidence in doing a final deal."

The crossbench peer added: "I think it leaves an impression that the Prime Minister hasn't got the authority to get through these difficult negotiations."

Former UK Brexit minister David Jones said "there will be people in Downing Street who will have regretted not making the position clearer with the DUP".

He urged ministers not to "ignore the parliamentary arithmetic" in which the DUP props up the minority Government, while making clear he also opposed regulatory alignment as it would hinder Britain's ability to strike new free trade deals around the world.

"I think we need to ensure that the DUP are on board with whatever is proposed and I think it's fairly clear that yesterday they were not on board - the fact that they managed to stall the negotiations yesterday, I think, demonstrates the precise strength of their position so I don't think it should be under-estimated at all," he s