NICOLA Sturgeon has challenged Ruth Davidson and David Mundell to keep to their word and resign from their positions if more customs controls are introduced between Northern Ireland and the rest of the UK in a move to prevent a hard Border in Ireland.

The Scottish Conservative leader and Scottish Secretary have told the Prime Minister they will step down if new controls are brought in as they believe these would boost the case for Scottish independence.

"Any differentiated deal that puts a hard Border down the Irish Sea they consider a resigning matter," senior Tory source told the Sunday Times.

Highlighting Davidson's and Mundell's position, the First Minister tweeted: "We’ll resign if you do anything that makes Scotland think there’s a better alternative to a hard Tory Brexit’ say Mundell and Davidson! First, what a bizarre position - isn’t it their job to stand up for Scotland? And, second, have they the gumption to resign? I bet they don’t!"

Theresa May faces a Tory mutiny and increased pressure from her DUP allies over Brexit as a key summit with EU leaders looms this week.

Former Brexit secretary David Davis said the plan to keep the UK in a customs union was "completely unacceptable" and urged Cabinet ministers to "exert their collective authority".

Meanwhile, Democratic Unionist Party leader Arlene Foster is reported to have said that a no-deal Brexit was now the most likely outcome after talks with senior figures including Michel Barnier in Brussels.

Her party is opposed to any customs arrangement which would result in extra checks on goods travelling to or from Great Britain. Foster says the move would amount to a different constitutional status for Northern Ireland, but her argument is rejected by Ireland and the rest of the EU, which says there are already some customs checks between Britain and Northern Ireland.

With continued speculation that Leave-supporting Cabinet ministers could resign if May presses ahead with the plan, David Davis said: "This is one of the most fundamental decisions that government has taken in modern times."

Writing in the Sunday Times he said: "It is time for the Cabinet to exert their collective authority. This week the authority of our constitution is on the line."

The issue of the border between Northern Ireland and Ireland is one of the last remaining obstacles to achieving a divorce deal with Brussels, with wrangling continuing over the nature of a "backstop" to keep the frontier open if a wider UK-EU trade arrangement cannot resolve it.

The European Union's version, which would see just Northern Ireland remain aligned with Brussels' rules, has been called unacceptable by May and is loathed by the DUP.

May's counter-proposal is for a "temporary customs arrangement" for the whole UK, but Tory Brexiteers are suspicious this could turn into a permanent situation, restricting the freedom to strike trade deals around the world.

The Sunday Times said at least nine ministers want May to change course when the Cabinet meets on Tuesday.

Speculation about possible resignations has centred on Andrea Leadsom, Penny Mordaunt and Esther McVey, as well as Mundell and Davidson.

May's own position also appeared in jeopardy, with as many as 44 letters demanding a vote of no confidence reportedly submitted to the Conservative 1922 Committee - just four short of the number required to trigger a ballot.

The Northern Ireland situation is politically problematic for May because her minority administration depends on the votes of the 10 DUP MPs.

A leaked email reported in the Observer indicated Foster was ready to block a Brexit deal.

According to a private email exchange between senior UK officials, seen by the newspaper, Foster gave her views during a dinner with the leader of Conservative MEPs, Ashley Fox.

The leaked email said Foster described the EU's chief Brexit negotiator Barnier as "difficult and hostile" and indicated "the DUP were ready for a no-deal scenario, which she now believed was the likeliest one".

A further demonstration of Tory resistance to May's plans came from MP Anne-Marie Trevelyan, who wrote in the Sunday Telegraph that "the idea of remaining in the customs union - even it if is called a 'temporary customs arrangement' - after the end of the transition period, in to the 2020s, means simply delaying Brexit and causing the 17.4 million people who voted for it to lose faith in our democracy".

Jacob Rees-Mogg, chairman of the European Research Group of pro-Brexit MPs, warned that when it came to the backstop proposal "temporary means eternal".

The UK and EU agreed in December, and again in March, that the withdrawal agreement would contain an Irish protocol in which a “backstop” solution for avoiding a hard border on the island of Ireland under any circumstances would be spelled out.

The EU has proposed that if a trade deal or bespoke technological solution for avoiding a hard border was not at hand by the end of the transition period, Northern Ireland would in effect stay in the single market and customs union as the rest of the UK withdraws.

May has insisted this would involve the constitutional dislocation of the UK. She is instead proposing a temporary EU-UK customs union, and for Northern Ireland to stay in the single market, should that be agreed at a later date by Stormont.