The British parliament's rejection of the Brexit agreement makes crashing out of the EU without a deal much more likely, the bloc said on Tuesday, as it warned there is no more it can do.

Lawmakers inflicted another crushing defeat on beleaguered Prime Minister Theresa May, voting to reject the divorce deal, even after she secured further guarantees from Brussels.

Senior EU officials lined up to voice regret at the result, and to hammer home the message that Brussels would not make any further concessions to help May win over recalcitrant MPs.

If parliament fails to approve an accord the UK will crash out of the bloc without a deal on March 29 - unless a delay is agreed, something the EU said it would be willing to consider.

A spokesperson for Donald Tusk, the president of the European Council, said he regretted the result, but warned that from Brussels' viewpoint "it is difficult to see what more we can do".

"With only 17 days left to March 29, today's vote has significantly increased the likelihood of a 'no-deal' Brexit," the spokesperson said.

The EU's chief Brexit negotiator Michel Barnier echoed the view, saying there was nothing more Brussels could do.

"The EU has done everything it can to help get the Withdrawal Agreement over the line. The impasse can only be solved in the UK. Our 'no-deal' preparations are now more important than ever before," Barnier tweeted.

'Uncharted waters'

The message was repeated by a spokesperson for European Commission President Jean-Claude Juncker.

"Given the additional assurances provided by the EU in December, January and yesterday, there is no more we can do. If there is a solution to the current impasse it has to be found in London," the spokesperson said.

EU ambassadors will meet in Brussels on Wednesday morning to assess the vote, the bloc's contingency plans - and to discuss whether to grant a delay to Brexit if London asks for one.

"We are in uncharted waters," one EU diplomat told AFP.

"We are not talking about a situation where there are still good solutions - we have to choose between different suboptimal solutions."

Shortly before the vote, Barnier voiced disquiet at the tenor of the debate in the House of Commons, warning MPs against the "dangerous illusion" that they could benefit from a transition period even without a proper divorce deal.

"Listening to debate in @HouseofCommons: there seems to be a dangerous illusion that the UK can benefit from a transition in the absence of the WA," Barnier tweeted, referring to the Withdrawal Agreement.

"Let me be clear: the only legal basis for a transition is the WA. No withdrawal agreement means no transition."

'Buckle up'

Transitional arrangements to wind down Britain's involvement with the EU form part of the agreement - but would need the British and European parliaments' approvals to take effect.

Some Brexit-supporting MPs argue that contingency measures announced by the EU that would come into effect in the event of no deal would effectively operate as a mini transition deal - a notion strongly rejected by Brussels officials.

Attention will now turn to whether Britain will ask for a delay to Brexit - a question MPs will be asked to vote on in the coming days.

"Should there be a UK reasoned request for an extension, the EU27 will stand ready to consider it and decide by unanimity," Juncker's spokesperson said.

An extension would need the backing of all 27 remaining EU countries.

Some countries, notably France, have insisted an extension would not be granted without good reason, but another EU diplomat said even if the arguments were shaky "we will probably still do it anyway".

"Now we have to buckle up a little tighter because the speed is getting higher so close to the Brexit date," the diplomat said.