BRUSSELS -- Leaders across the European Union offered a united chorus of "No" on Wednesday to Britain's belated bid to negotiate changes to the Brexit divorce deal so Prime Minister Theresa May can win the backing of her Parliament. In London, May acknowledged that her government hasn't decided exactly how it will try to change the deal to address British lawmakers' concerns about the Irish border.

All this while Britain is headed for the EU exit in less than two months, on March 29.

"We are, quite simply, running out of road," said Irish Foreign Minister Simon Coveney.

Buoyed by winning a vote in Parliament, May has vowed to secure "legally binding changes" to the withdrawal agreement. British lawmakers voted Tuesday to send May back to Brussels seeking to replace an Irish border provision in the deal with "alternative arrangements," ignoring EU warnings that the agreement cannot be altered.

"The withdrawal agreement will not be renegotiated," said Jean-Claude Juncker, chief of the EU's executive arm, the European Commission.

Juncker told European parliamentarians in Brussels "the withdrawal agreement remains the best and only deal possible."

Irish Prime Minister Leo Varadkar said that "we've been down that track before and I don't believe that such alternative arrangements exist."

Much of the opposition centres on a border measure known as the "backstop," a safeguard mechanism would keep the U.K. in a customs union with the EU to remove the need for checks along the border between the U.K.'s Northern Ireland and EU member Ireland after Brexit.

The border area was a flashpoint during decades of conflict in Northern Ireland that cost 3,700 lives. The free flow of people and goods across the near-invisible border underpins both the local economy and Northern Ireland's peace process.

Many pro-Brexit British lawmakers fear the backstop will trap Britain in regulatory lockstep with the EU, and say they won't vote for May's deal unless it is removed.

German government spokesman Steffen Seibert said "opening up the withdrawal agreement is not on the agenda."

Britain and the EU struck a divorce deal in November after a year and a half of tense negotiations. But the agreement has run aground in Britain's Parliament, which overwhelmingly rejected it on Jan. 15.

May was due to speak to Varadkar and European Council President Donald Tusk on Wednesday, and met opposition Labour Party leader Jeremy Corbyn in an attempt to find elusive cross-party unity on Brexit.

May conceded that her government hadn't settled on a way to replace the backstop, telling lawmakers that "there are a number of proposals for how that could be done." May said measures under consideration included a unilateral exit mechanism from the backstop for Britain, a time limit to the backstop and "mutual recognition and trusted trader schemes."

The EU says the backstop is an insurance policy and as such can't have a time limit or a get-out clause.

Chief EU Brexit negotiator Michel Barnier said that "frankly, no one from either side is able to say precisely, in a clear way, what the nature of these alternative arrangements would be, whether they would be workable and effectively fulfil the aims of the backstop."

The EU parliament's point-man on Brexit, Guy Verhofstadt, underlined that nobody in Europe wanted to use the backstop, but that it's "needed to be 100 per cent sure that there is no border between Northern Ireland and the Irish republic."

Verhofstadt said the only way for May to win concessions would be to back away from her long-held stance that Britain would not remain part of the EU's customs union after Brexit.

"If the future relationship is, for example, a customs union, that makes it completely different," Verhofstadt told reporters.

The impasse has left Britain lurching toward its EU exit without a deal to ease the way. Many businesses fear economic chaos will ensue if the U.K. isn't covered by existing EU trade agreements or a new agreement, leading to tariffs, customs checks and other barriers between the U.K. and the EU.

British lawmakers approved a motion Tuesday ruling out a "no-deal" Brexit but without saying how they expect their preference to be achieved. The vote was not legally binding, but has political force as an expression of the will of Parliament.

Juncker said the vote by Britain's Parliament "has further increased the risk of a disorderly exit of the U.K."

"We know from yesterday's debate that the House of Commons is against many things," Juncker said. "It is against a no-deal Brexit, it is against a backstop.

"But we still don't know what exactly the House of Commons is for."

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Jill Lawless reported from London. Lorne Cook contributed from Brussels