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Ruth Davidson, the highly-regarded pro-European leader of the Scottish Tories, and her ally David Mundell, the Scottish secretary, have told May in writing they will resign their positions if there is a hard border between Northern Ireland and the UK after Brexit.

They have told May that agreeing to a deal which allows Northern Ireland to remain in a form of customs union with Ireland and the rest of the EU but excludes the rest of the UK, would fuel calls for Scottish independence.

It would strengthen the case being made by Nicola Sturgeon that promises made in the 2014 independence referendum about preserving the UK’s internal market were worthless, they warned the prime minister.

They have told May:

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.

Sturgeon is making a major speech to the Royal Academy of the Arts on Monday where she will underscore the significance of that stance for Scotland, which voted heavily for remain in June 2016, by again demanding the UK remains in both the single market and customs union.

Two of the most committed pro-European Tories, Davidson and Mundell’s threats are designed to shore up the government’s Europhile wing as a counterweight to the demands from Brexiteers in the party for a hard Brexit deal.

Their letter continues:

Any deal that delivers a differentiated settlement for Northern Ireland beyond the differences that already exist on 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. [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.

Nicola Sturgeon may be updating her RSA speech in light of today’s fast-moving events, but in an advance text released by the Scottish government, she urged May to recognise there was a cross-party coalition which supported a softer Brexit. She said:

It [is] simply incorrect for the prime minister to say that there is no alternative to Chequers. In fact, the UK government’s position is increasingly absurd. Insisting on pursuing proposals they have been told will not work while rejecting a plan that will. With crucial decisions coming up over the next few weeks and months at EU level - and in the House of Commons where the UK government must seek the approval of the UK parliament - it is vital to break the deadlock. For the prime minister and the UK government it is time to face reality. For MPs at Westminster it is time to come together in a common sense coalition to minimise the Brexit damage.