The British parliament's decision to demand changes to the Brexit withdrawal deal had increased the risk of a messy "no deal" divorce, the president of the European Commission, Jean-Claude Juncker, warned on Wednesday.

"Yesterday's vote increased the risk of a disorderly withdrawal," he told a sitting of the European Parliament.

"We need to be ready for all scenarios, including the worst."

Speaking at a debate, the EU Commission president reiterated the EU position that the withdrawal agreement already signed last year with Prime Minister Theresa May cannot be re-negotiated.

And, while he said he would "work day and night" to head off the danger of a no-deal divorce, Tuesday's debate in the House of Commons had not changed anything and Europe remains united in support of the agreement.

He insisted that the so-called "Irish backstop", opposed by eurosceptic British MPs, must remain in the deal as an insurance against the return of a hard border on Ireland and against "slipping back into darker times past."

Having thrown out the exit deal May negotiated with the EU, divided British lawmakers voted 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 on the terms of the split, vowing to return to Brussels to demand changes to the text.

In an earlier reaction, Irish foreign minister Simon Coveney told RTE radio: "It's 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'."