MPs hoping for a Boudica moment from Theresa May in the House of Commons on Monday would have been disappointed as she responded to the failure of Brexit talks on Sunday with a call for cool, calm heads to prevail.

Donald Tusk waited until she had finished speaking before sending his invitation letter for this week’s summit to EU leaders and inviting May to address them before dinner on Wednesday evening.

In the hours after Dominic Raab told Michel Barnier on Sunday that Britain could not accept the deal that was tacitly agreed by negotiators, the EU waited to see how Downing Street would spin the setback. May’s conciliatory tone, stressing how much the two sides agreed on, evoked a similarly optimistic response from Tusk, who urged EU leaders not to give up on the deal.

The two sides agree on much about the backstop and the EU has accepted Britain’s proposal that its customs element should include the whole of the UK. In the deal on the table in Brussels, however, the legally-binding withdrawal agreement would have included a Northern Ireland-only backstop, with a commitment to establish a UK-wide customs arrangement as part of the future relationship between the EU and the UK.

BREXIT: The Facts Read them here

When attorney general Geoffrey Cox saw this proposal last Thursday, he reportedly pointed out to May and her senior ministers that their UK-wide customs backstop would sit in the non-binding political declaration accompanying the withdrawal agreement. Britain acknowledges that the backstop can’t have a specific end date but it has proposed other mechanisms for determining when it should end, which the EU has rejected.

‘Backstop to a backstop’

And the EU insists that, regardless of the shape an all-UK customs backstop eventually takes, there must still be an “all weather”, Northern Ireland-specific backstop written into the withdrawal agreement. This original backstop is what the prime minister and her officials are referring to when they speak of a “backstop to a backstop”.

Both the prime minister and her officials focused exclusively on Monday on the customs element of the backstop rather than on what it says about the regulation of goods. This would appear to confirm, as some EU sources suggest, that the two sides have agreed on the regulatory element of the backstop.

The DUP’s Nigel Dodds sought an assurance from the prime minister on Monday that there would be no differentiation on regulation or customs between Northern Ireland and the rest of the UK but she offered only a vague response.

The DUP remains suspicious of May and Brexiteers on her backbenches and within the cabinet are poised to revolt once the details of a deal with the EU emerge. But just as the debacle at Salzburg last month saved her from a rebellion during the Conservative party conference, Sunday’s failure has ensured the prime minister an easier time at cabinet on Tuesday.

A Brexit deal is clearly within reach if the prime minister wishes to grasp it but she knows she can’t win enough support in her party right now to ensure parliamentary approval. What remains uncertain is whether more time will bring new concessions from the EU or increase pressure on MPs to back her plan rather than risking a no-deal Brexit.