Brexit: Theresa May faces backlash from Brussels over Withdrawal Agreement renegotiation

But senior figures in Brussels, Berlin, Paris and Dublin resisted the demand from Mrs May as the clock ticks down to the UK's departure from the European Union on March 29.

The Prime Minister also clashed with Jeremy Corbyn in the Commons ahead of private talks with the Labour leader on the Brexit process.

Having boycotted earlier cross-party talks, the Labour leader said he was ready to discuss a "sensible" approach to Brexit after MPs voted on Tuesday night to rule out no deal.

Mr Corbyn demanded to know which of her red lines she was prepared to compromise on in order to avoid a no-deal Brexit.

"It really is time that the Prime Minister acknowledged she has got to move on from the red lines she put down in the first place," he said.

READ MORE: Theresa May accused of 'presiding over a rising tide of racism in the UK' 

But Mrs May told Mr Corbyn he had opposed "every move by this Government to get a deal" and "he is the one risking no deal".

In dramatic scenes on Tuesday night, MPs voted by a margin of 317 to 301 to back a plan - the "Brady amendment" - which requires the PM to replace the Agreement's controversial backstop with "alternative arrangements" to keep the Irish border open after Brexit.

But asked five times on BBC Radio 4's Today programme what this "alternative" involved, Brexit Secretary Stephen Barclay was unable to provide any specific explanation.

Mr Barclay said the UK was "exploring in terms of the use of technology... looking at things like the time limit" to deal with the backstop.

He added: "There are a number of options, there are issues in terms of having time limits, issues in terms of exit clauses, issues in terms of technology, and this will be the nature of the negotiation with the European Union in the coming days."

READ MORE: PMQs: Theresa May claims Jeremy Corbyn is 'risking a no-deal Brexit' 

Downing Street has suggested that the UK's position could involve a time-limit or exit clause to the backstop or swapping it for a free trade agreement, as proposed in the so-called Malthouse Compromise drawn up by MPs from the Tories' Remain and Leave wings.

But the suggestion that the deal struck between the Government and Brussels could be unpicked was rejected by senior figures across the EU.

European Council president Donald Tusk will speak by phone with Mrs May on Wednesday evening.

Following Tuesday night's votes in the House of Commons, Mr Tusk's spokesman said: "The backstop is part of the Withdrawal Agreement, and the Withdrawal Agreement is not open for renegotiation."

Brussels' chief Brexit negotiator, Michel Barnier, told reporters that the EU's position was "very clear", while Irish foreign minister Simon Coveney said the backstop remained "necessary". French President Emmanuel Macron said the Withdrawal Agreement was "not renegotiable".

European Commission vice-president Frans Timmermans said there was "an increasing risk" that the UK will leave without a deal in March.

"We continue to urge the UK Government to clarify its intentions with respect to its next steps as soon as possible," he added.

The European Parliament's chief Brexit negotiator, Guy Verhofstadt, expressed frustration with the British: "What needs to stop is this: An amendment with 10 votes for, then an amendment with 10 votes against, an amendment that barely pulls through, one that fails... That is no way to build a future relationship with the EU."

READ MORE: Ian Blackford: Calls for permission to hold Indyref2 'must be accepted by UK Government 

Germany's foreign minister, Heiko Maas, said: "Germany and the entire Union are firmly on Ireland's side. We will not allow Ireland to be isolated on this issue."

French Europe minister Nathalie Loiseau said: "The Withdrawal Agreement that is on the table is the best possible agreement. Let us not reopen it."

Mr Barclay claimed that Tuesday night's amendments, two weeks after Mrs May suffered the heaviest parliamentary defeat in modern history over the meaningful vote, had "overturned a defeat of 230 into a victory".

But there was concern from the business community, with CBI director general Carolyn Fairbairn describing the Brady amendment as "a throw of the dice" and warning that firms were having to accelerate expensive no-deal preparations.

Brexiteer ringleader Jacob Rees-Mogg made clear on Wednesday that he remains prepared to see the UK leave without a deal on March 29 if the EU refuses to reopen negotiations.

"If (the EU) think the Withdrawal Agreement is non-negotiable then we will have to leave without an agreement," he told TalkRadio. "Do they want the £39 billion, do they want an agreement... or us just to leave? It's up to them."