THERESA May returned to London last night after failing to persuade European Union chiefs to make any changes to the Irish backstop in her Brexit deal.

The Prime Minister travelled to talks in Brussels yesterday in a bid to urge EU leaders to re-open the withdrawal agreement after it was heavily defeated last month in the Commons.

Donald Tusk, the president of the European Council, which represents the leaders of the 27 other members of the bloc, tweeted afterwards: “Meeting PM @theresa_may on how to overcome impasse on #brexit. Still no breakthrough in sight. Talks will continue.”

Tory Brexiteers have refused to back May’s deal unless the backstop is removed or changed in a legally binding way. They say it keeps the UK in indefinite alignment with EU laws and prevents the UK winning its own trade deals across the world.

The EU, however, say it is necessary, as an insurance policy to maintain an open border in Ireland regardless of what happens in the Brexit process.

May’s encounter with Tusk was expected to be frosty after the former Polish prime minister attacked Brexiteers on Wednesday following a meeting with Irish premier Leo Varadkar, who opposes any changes to the backstop.

After his talks with Varadkar, Tusk reaffirmed his commitment to an open border and the Irish peace process, adding: I’ve been wondering what that special place in hell looks like for those who promoted Brexit, without even a sketch of a plan how to carry it out safely.”

Earlier May described as “robust but constructive” talks with European Commission president Jean-Claude Juncker.

Juncker underlined that the withdrawal agreement thrashed out between the EU and May would not be redrawn, but held open the possibility of adding “more ambitious” wording to a non-legally binding document setting out plans for the future relationship.

Following talks with Juncker, a joint statement said: “The discussion was robust but constructive.

READ MORE: Jeremy Corbyn accused of facilitating a ‘hard Tory Brexit'

The National: uropean Commission president Jean-Claude Juncker is set for another round of talks with Mayuropean Commission president Jean-Claude Juncker is set for another round of talks with May

Despite the challenges, the two leaders agreed that their teams should hold talks as to whether a way through can be found that would gain the broadest possible support in the UK Parliament and respect the guidelines agreed by the European Council.”

Brexit Secretary Stephen Barclay and EU chief negotiator Michel Barnier will meet next Monday, while Juncker and May will have another meeting before the end of the month to take stock of the situation.

May set out MPs’ demands for a “legally binding change to the terms of the backstop”, while Juncker “underlined that the EU27 will not re-open the withdrawal agreement”.

But he “expressed his openness to add wording to the Political Declaration” to be “more ambitious in terms of content and speed when it comes to the future relationship”.

In diplomatic statements, the description “robust” often indicates a heated row.

READ MORE: Why a no-deal Brexit could see return of EU roaming charges

The spokesman for the European Commission Margaritis Schinas said that the word was “something that both sides agreed was an accurate way to describe the tonality of the meeting”.

As May arrived in Brussels a protester waving a placard reading “Don’t crash out” leaped in front of the PM’s convoy as it arrived at the Commission’s Berlaymont HQ but was quickly whisked away.

May was offered a chink of light by German chancellor Angela Merkel, who again ruled out re-opening the withdrawal agreement, but said she believed “solutions” could be found.

Speaking during a visit to Slovakia, Merkel said: “I think we can find solutions without re-opening the withdrawal agreement.”

Meanwhile, it emerged May wants to delay another Commons “meaningful vote” until the end of February – a month before the UK is scheduled to leave the EU on March 29.