British opposition Labor Party leader Jeremy Corbyn moved a step closer to paving the way for another referendum on European Union (EU) membership by trying to use parliament to grab control of Brexit from Prime Minister Theresa May.

With the clock ticking down to March 29, the date set in law for Brexit, the UK is in the deepest political crisis in half a century as it grapples with how, or even whether, to exit the European project it joined in 1973.

After May's Brexit divorce deal was rejected by 432-202 lawmakers last week, the biggest defeat in modern British history, some lawmakers are trying to take control of Brexit from May's weakened minority government.

Labor put forward an amendment seeking to force the government to give parliament time to consider and vote on options to prevent a 'no deal' exit - a course May has repeatedly refused to rule out.

Among the options, Labor said, should be a permanent customs union with the EU and "a public vote on a deal" - both proposals that May has ruled out.

"It is time for Labor's alternative plan to take center stage, while keeping all options on the table, including the option of a public vote," Corbyn said.

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

However, Labor's business spokeswoman Rebecca Long-Bailey said the amendment did not mean that the party supported a second vote and merely reflected its existing policy.

"If it was passed, the amendment, and it went to a vote on these specific issues then that would be a decision for the party to take at the time," she told BBC radio.

Lawmakers will debate and vote on the next steps on January 29.

May on Monday proposed tweaking her deal, a bid to win over rebel Conservative lawmakers and the Northern Irish party which props up her government, but Labor said May was in denial about the crushing defeat of her plans.

She said another referendum would strengthen the hand of those seeking to break up the UK and could damage social cohesion by undermining faith in democracy.

UK Brexit minister: We are working on what to ask from the EU

Britain is still working on what to ask from the EU to allay lawmaker concerns over the backup plan that aims to prevent a hard border on Ireland, Brexit minister Stephen Barclay said on Tuesday.

When asked on BBC television what Britain's specific proposal was, he said: "We are working on that as part of the listening exercise."

The EU doesn't want to be in a situation of having no deal, Barclay said, adding May's deal, which suffered the biggest defeat in modern British history last week, is the most popular of choices available.

Germany calls for UK's orderly exit 

German Justice Minister Katarina Barley, who has both German and British citizenship, said on Tuesday she was disappointed by May's plan to break a deadlock over Brexit and suggested Britain hold a second referendum.

Michael Roth, German minister for European affairs, also expressed his disappointment with May's speech, saying on Twitter: "Where is the plan B? Just asking for a friend…" 

A German government spokesman said late on Monday that Germany continued to advocate for an orderly exit and that it expected the British government to agree soon on proposals that are backed by a majority of parliament.

(Cover: Labor Leader Jeremy Corbyn gives a speech at a rally at St Mary's in the Castle, January 17, 2019. /VCG Photo)