Embattled UK Prime Minister Theresa May faces another day of Brexit grilling before legislators on Tuesday with the opposition Labour Party opening the door for a new referendum on leaving the European Union.

UK legislators will debate and vote on the next steps of the EU divorce on January 29, and before that they can put forward amendments to the government's plan, seeking to shape Britain's exit from the bloc.

Labour Party's leader Jeremy Corbyn submitted an amendment late Monday seeking to force the government to allow Parliament to consider and vote on options to prevent Britain leaving on March 29 without an agreement.

Among those options should be a permanent customs union with the EU - and a second referendum on Brexit, the party said. It was the first time Corbyn formally suggested the possibility of a new vote.

"The prime minister is both refusing to change her red lines or take the threat of a no deal exit off the table. MPs must now act to break the deadlock," he said in a statement.

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"Our amendment will allow MPs to vote on options to end this Brexit deadlock and prevent the chaos of a no deal."

German Justice Minister Katarina Barley said on Tuesday she was disappointed by May's plan to break a deadlock over Brexit and called on Britain to hold a second referendum.

But UK Brexit Secretary Stephen Barclay said going back on the original vote would damage democracy.

'Groundhog Day'

Groups of "soft Brexit"-backing legislators - who want to keep close economic ties to the bloc - are planning to use amendments to try to rule out a "no-deal" Brexit and make May ease her insistence that leaving the EU means quitting its single market and customs union.

Corbyn said his party had prepared its own plan for a "new, comprehensive customs union with the EU" and "would not rule out" the option of a second public vote on Brexit.

He accused May on Monday of being in "deep denial" about her doomed deal.

"This really does feel a bit like Groundhog Day," he said, referring to the 1993 film starring Bill Murray, in which a weatherman is fated to live out the same day over and over again.

With just two months before the UK is due to leave the bloc, May added she will press on with efforts to get an EU divorce bill approved by Parliament. May said the EU is "very unlikely to extend Article 50 without a plan for a deal".

The UK is set to leave the 28-member bloc on March 29, two years after it triggered Article 50 - the exit clause in the EU's constitution - and kick-started negotiations with European leaders over a divorce deal.

"There is widespread concern about the possibility of the UK leaving without a deal. There are those on both sides that want the government to rule this out," said May.

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"But we need to be honest with the British people about what that means. The right way to rule out a no-deal Brexit is for this house to approve a deal with the EU. That is what this government is seeking to achieve."

Way forward?

On Monday, May rejected calls from pro-EU legislators to delay Britain's departure from the bloc or to hold a second referendum on whether to leave.

After her Brexit deal was thrown out last week by a crushing 432-202 vote in Parliament, May said she would consult legislators from all parties to find a new way forward.

But Corbyn called the cross-party meetings a "stunt" and other opposition leaders said the prime minister didn't seem to be listening.

May also said the government had decided to waive a 65 pound ($84) fee for EU citizens in Britain who want to stay permanently after Brexit.

Al Jazeera's Laurence Lee, reporting from outside the House of Parliament in London, said it appeared May's strategy was "to run the clock down until March 29".

"May wants to scare the life out of politicians from all sides with the prospect of a no-deal then bounce them into saying the deal's deeply flawed, but it's better than staying in the European Union," he said.

Brexit drama

Brexit supporters say while there may be some short-term disruption, in the long term, the UK will thrive outside what they cast as a doomed experiment in German-dominated unity and excessive debt-funded welfare spending.

May said she had heeded legislators' concerns over an insurance policy known as the "backstop" that is intended to guarantee there are no customs checks along the border between EU member Ireland and the UK's Northern Ireland after Brexit.

May told the House of Commons she would be "talking further this week to colleagues ... to consider how we might meet our obligations to the people of Northern Ireland and Ireland in a way that can command the greatest possible support in the House".

"And I will then take the conclusions of those discussions back to the EU," she said.

The EU says it will not renegotiate the deal struck with May.

The EU, which has an economy more than six times the size of the UK, says it wants an orderly exit, but senior officials have expressed frustration at London's crisis.

German Europe Minister Michael Roth said on Monday even William Shakespeare would not have been able to think up a Brexit tragedy of such drama.