European Union leaders offered a united chorus of 'No' on Wednesday to Britain's belated bid to negotiate changes to the Brexit divorce deal, with one official calling on British lawmakers to stop bickering and work out a cross-party approach.

In London, Prime Minister Theresa 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,' Irish Foreign Minister Simon Coveney said.

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 can't be altered.

But EU leaders saw the House of Commons session in a very different light.

Jean-Claude Juncker, chief of EU executive arm the European Commission, said Tuesday's vote 'has increased the risk of a disorderly withdrawal of the United Kingdom' from the EU.

'The withdrawal agreement will not be renegotiated,' he said.

Other EU governments backed that stance, leaving little room for May to realistically secure any changes to the Brexit deal.

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

Much of the opposition centers on a border measure known as the 'backstop,' a safeguard mechanism would keep the UK in a customs union with the EU to remove the need for checks along the border between the UK'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.

May was speaking to Ireland's 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 fulfill 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 percent 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.

Corbyn, who heads Britain's left-wing main opposition party, said he 'set out the Labour case for a comprehensive customs union with the European Union' during talks with May.

He called the talks 'serious' but accused the government of 'running down the clock' to force lawmakers to choose between May's deal and a 'no-deal' Brexit in March 29.

Verhofstadt called for a cross-party approach in Britain, saying he hoped the meeting between the Conservative and Labour leaders will yield something more than 'only eating biscuits and drinking tea.'

If they start working together, he said, 'it could be the solution to this problem.'

Many businesses fear economic chaos will ensue if the UK isn't covered by existing EU trade agreements or a new agreement, leading to tariffs, customs checks and other barriers between the UK and the EU.

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

Juncker called on British lawmakers to make clear what they want.

'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.'