European leaders moved Wednesday to head off British Prime Minister Theresa May's bid to rewrite the Brexit divorce deal, warning they will not budge.

Having thrown out the exit deal May negotiated with the EU, divided British lawmakers voted on Tuesday to send her back to get an Irish border "backstop" clause removed.

May seized on this as a chance to prevent Britain crashing out of the European Union on March 29 without an agreement, vowing to return to Brussels to demand changes to the text.

But even she admits she faces a formidable challenge convincing Brussels to re-open an accord that took 18 excruciating months to conclude, and European leaders are so far united in dismissing any such manoeuvre.

"My message to PM @theresa_may: The EU position is clear and consistent. The Withdrawal Agreement is not open for renegotiation," EU Council President Donald Tusk tweeted.

"Yesterday, we found out what the UK doesn't want. But we still don't know what the UK does want," he added.

Irish foreign minister Simon Coveney said it was "an extraordinary situation when a prime minister and a government negotiates a deal and then goes back and during the ratification process votes against their own deal".

"That's like saying in a negotiation, 'Well either you give me what I want or I'm jumping out of the window'," he told RTE radio.

Other frustrated EU officials including Brexit negotiator Michel Barnier insisted the remaining 27 EU members were united and determined not to abandon the backstop clause they believe is key to maintaining peace on the border.

European Commission president Jean-Claude Juncker addressed the European Parliament to push home the message that the withdrawal agreement would not be re-negotiated.

And he warned that the British vote had only "increased the risk of a disorderly withdrawal" and of Northern Ireland "slipping back into darker times past".

Echoing earlier warnings from French President Emmanuel Macron and Austrian Chancellor Sebastian Kurz, German leader Angela Merkel's spokesman said reopening the deal was "not on the agenda".

And Irish Prime Minister Leo Varadkar insisted "renegotiation is not on the table".

Threat of 'no deal'

May's spokesman said she had been aware that "this wasn't going to be an easy process" but that: "What the vote has actually done is set out what parliament requires in order to be able to pass this vote."

The "backstop" written into the negotiated deal is seen by EU leaders as an insurance policy against disrupting the Irish peace process.

It could legally lock the UK into EU trade rules indefinitely in order to keep the Irish border free-flowing.

Guy Verhofstadt, who heads the European Parliament's six-member Brexit steering group, said the backstop clause was "absolutely needed" and there was hardly room to change the deal.

Going further, group member Philippe Lamberts was scathing.

"Saying you're against the backstop is like saying you're against bad weather. You might not like it, but you can't change it," he said.

But a British MEP, Ashley Fox of May's Conservatives, warned that after Tuesday's vote the backstop was more of a threat than an insurance policy.

"The backstop will create a hard border, not prevent one," he said, arguing that British lawmakers would never accept the clause and so it would lead to a no deal Brexit and renewed border controls.

'Throw of the dice'

London stocks rallied and the pound rebounded slightly after suffering heavy losses on fears of Britain leaving the EU without a deal.

Carolyn Fairbairn, who heads the Confederation of British Industry lobby group, said: "Renegotiation is a throw of the dice. It must succeed or fail fast."

Tuesday night's parliamentary amendment called for the backstop to be replaced with "alternative arrangements to avoid a hard border" -- vague wording that did not pin May to any approach.

Also Tuesday, MPs backed a non-binding measure that "rejects the United Kingdom leaving the European Union without a withdrawal agreement".

But they threw out another plan seeking to oblige May to request a delay to Brexit if no new deal with the EU emerges by February 26.

Corbyn meeting

May said parliament's approval of the backstop amendment gave her a "mandate" to "seek to obtain legally binding changes to the withdrawal agreement" and promised to give MPs a chance to vote on February 14 on what happens should she fail to win a new agreement.

On Wednesday, she met British opposition leader Jeremy Corbyn for what her spokesman said were "serious and engaged" talks on the way ahead.

Later Wednesday May tweeted that she "stressed to him the importance of the UK being able to do our own trade deals, and emphasised that the only way to avoid No Deal is to vote for a deal".