Britain is to have talks with the EU over the coming days about how to obtain “further assurances” which might persuade MPs to back the Brexit Withdrawal Agreement, Theresa May has said.

In a press conference at the end of a European Council summit in Brussels, the Prime Minister acknowledged that it would not be possible to reopen the agreement to alter the backstop provisions which have sparked mass rebellion among Tory MPs.

She confirmed she had a “robust” discussion with European Commission president Jean-Claude Juncker and insisted she had been “crystal clear” about the UK’s need for firmer assurances that the backstop cannot become permanent.

Video footage of the conversation showed a clearly angry PM apparently berating Mr Juncker for suggesting that her message on Brexit had been “nebulous”.

She told the press conference: “I had a robust discussion with Jean-Claude Juncker – I think that’s the sort of discussion you’re able to have when you have developed a working relationship and you work well together.

“And what came out of that was his clarity that actually he’d been talking – when he used that particular phrase – he’d been talking about a general level of debate.”

Mr Juncker later insisted he was referring not to the Prime Minister but the “overall state of the debate in Britain” and said their differences had been settled with a kiss.

“In the course of the morning after having checked what I said yesterday night, she was kissing me,” he said.

Mr Juncker stressed that the EU leaders had “the highest respect” for Mrs May and sympathised with her over the threat to her position from her own MPs.

And European Council president Donald Tusk said: “My impression is that in fact we have treated Prime Minister May with much greater empathy and respect than some British MPs, for sure.”

Mrs May welcomed the official conclusions issued by the EU27 which committed the EU to trying to get a post-Brexit trade deal agreed quickly enough to avoid the need for a backstop to keep the Irish border open.

“As formal conclusions, these commitments have legal status and therefore should be welcomed,” she said.

But she added: “The EU is clear, as I am, that if we are going to leave with a deal, this is it.

“But my discussions with colleagues today have shown that further clarification and discussion following the council’s conclusions is in fact possible.

“There is work still to do and we will be holding talks in coming days about how to obtain the further assurances that the UK Parliament needs in order to be able to approve the deal.”

However German Chancellor Angela Merkel insisted it was for Britain to take the next steps, saying: “The 27 member states have given assurances. They are contained in the conclusions of yesterday evening.

“That is our position. That is what we have put on the table. And now we expect Great Britain to respond.”

Belgium’s PM Charles Michel said: “The ball is now politically in the British court.”

And Mr Tusk said he had “no mandate” to organise any further negotiations.

Mrs May’s hopes of a legally binding commitment on the backstop from the EU27 were dashed on Thursday, when Mr Juncker said there could be “no real changes” to the Withdrawal Agreement negotiated over 18 months.

The Prime Minister addressed the EU27 leaders on Thursday about MPs’ concerns  about the backstop which had prevented her getting her Brexit deal through Parliament this week.

Mr Tusk said the leaders had expressed a “firm determination” to work “speedily” to ensure there is an agreement on the future relationship in place by the time the transition period ends in December 2020, so the backstop is not needed.

But Mr Juncker criticised Britain’s lack of clarity over what it was seeking from the future relationship.

“Our UK friends need to say what they want, instead of asking us to say what we want,” he said.

“So we would like, within a few weeks, our UK friends to set out their expectations for us because this debate is sometimes nebulous and imprecise and I would like clarifications.”

Belgium EU Brexit
European Commission president Jean-Claude Juncker embraces council president Donald Tusk at the Brussels summit (Stephanie Lecocq/AP)

The EU hardball approach appears to leave Mrs May with limited room for manoeuvre during the countdown to the UK’s departure on March 29.

The Prime Minister told the summit that a package of assurances around the backstop could “change the dynamic” at Westminster.

At the same time, she made clear a failure by EU leaders to offer concessions risked the collapse of the whole agreement, with the UK leaving in March in a disorderly, no-deal Brexit.

Mrs May managed a smile at her press conference when a reporter asked if she had had a “trying week”, jokingly replying: “Has something happened this week?”

When asked whether the problems with her party at home and dealing with the EU had made her want to quit as leader, she said it is “our duty as a Government and as a Parliament” to see Brexit through.

She added: “I never said it was going to be easy.

“Negotiations like this are always tough. There are always difficult times and as you get closer to the very end, that can get even more difficult because you are sorting out the last details of something.”

Opposition leader Jeremy Corbyn said Mrs May’s plan was “dead in the water” after she “utterly failed in her attempts to deliver any meaningful changes”, and reiterated Labour’s call for it to be put to a vote before Christmas.

Cabinet Office Minister David Lidington rejected that idea and defended Mrs May’s handling of the talks, telling Today: “Anybody who has heard Theresa May in debate, anybody who has heard her around the Cabinet table, knows there is a very clear plan.”

He described the talks as “a welcome first step that was the removal of uncertainty” over the EU’s intentions, because it has shown it wants a “speedy UK trade deal” that would remove the need for the backstop in the first place.