In a statement from European Council president Donald Tusk, speaking on behalf of the 27 other EU member states, Brussels made clear the backstop could not be stripped from the withdrawal agreement.
“The withdrawal agreement is and remains the best and only way to ensure an orderly withdrawal of the UK from the EU,” Mr Tusk said moments after the final vote in the House of Commons.
“The backstop is part of the withdrawal agreement and the withdrawal agreement is not open for re-negotiation.”
He added: “We continue to urge the UK government to clarify its intentions with respect to its next steps as soon as possible.”
French president Emmanuel Macron was the first European leader to respond to Mrs May’s plans, saying before last night’s votes that the withdrawal agreement, including the Irish backstop, “is the best accord possible”. “It is not re-negotiable,” he said.
On a visit to Cyprus, Mr Macron said a no-deal Brexit was a situation “no-one wants, but we should all prepare for”.
Senior politicians around Europe warned that seeking to renegotiate the Irish border “backstop” would also mean re-opening other parts of the deal, including the economic status of Gibraltar.
Manfred Weber, the leader of the biggest group in the European Parliament, noted the existing deal was a “compromise between many interests”.
Mr Weber said: “If there is now a unilateral attempt to reopen the agreement, the consequence will be that not just the backstop has to be renegotiated – then the Gibraltar question, the question of how much money Britain has to pay for exiting, the question of citizens’ rights will have to be renegotiated.”
Mr Weber, the German leader of the European People’s Party, added: “If we reopen [it], then everything will be reopened.
“And to be honest, I don’t see much sense in that.”
Before last night’s votes in the House of Commons, Germany’s justice minister said there was no room for substantial renegotiation.
Katarina Barley said the EU could be flexible on Britain’s departure date, but insisted London must have a plan for a delay to make sense.
Ms Barley said it would be “difficult” if they wanted to renegotiate “because the EU cannot make more concessions to Britain on the important points”.
She said the EU would be prepared to compromise, but “if there is no plan at all for what should then be different, then a delay makes only very limited sense”.
Ms Barley, who is half-British and has long advocated a second referendum on EU membership, added in a radio interview that revisiting the Brexit vote was “becoming more likely every day” given the political situation in Britain.