NICOLA Sturgeon has challenged Ruth Davidson and David Mundell to keep to their word and resign 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 written to the Prime Minister saying they will step down if new controls are brought in as they believe these would boost the case for Scottish independence, according to a report yesterday.

“Any differentiated deal that puts a hard border down the Irish Sea they consider a resigning matter,” a 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!”

Labour’s Ian Murray described their stance as “contemptible”.

He tweeted: “They also don’t want to continue to participate in the customs union and single market so how do they suggest resolving [the border issue?] Utterly contemptible. They can’t achieve a no hard border in Ireland without participation in the same trading arrangements as the EU.”

In their letter, Davidson and Mundell said “the integrity of the United Kingdom’ was their top priority.

They said: “Having fought just four years ago to keep our country together, the integrity of our United Kingdom remains the single most important issue for us in these negotiations.

“Any deal that delivers a differentiated settlement for Northern Ireland beyond the differences that already exist on an all Ireland basis (eg agriculture), or can be brought under the provisions of the Belfast Agreement, would undermine the integrity of our UK internal market and this United Kingdom.”

The letter adds: “We could not support any deal that creates a border of any kind in the Irish Sea and undermines the Union or leads to Northern Ireland having a different relationship with the EU than the rest of the UK, beyond what currently exists.”

The report comes as Theresa May faces another crisis with cabinet ministers such as Andrea Leadsom and Esther McVey also threatening to resign, while former Brexit Secretary David Davis has urged other ministers to revolt against her Brexit plans.

Meanwhile, DUP leader Arlene Foster is reported to have said a no-deal Brexit is 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 Britain.

Foster says the move would amount to a different constitutional status for Northern Ireland, but her argument has been rejected by Ireland and the rest of the EU, which says there are already some customs checks between the two.

With speculation that Leave-supporting 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.”

The issue of the border between Northern Ireland and the Irish Republic is one of the last remaining obstacles to achieving a withdrawal deal with the EU, 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 EU’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.