UK Prime Minister Theresa May on Tuesday offered lawmakers the chance to vote in just over two weeks' time on whether to delay Brexit or go for a potentially disorderly no-deal exit from the European Union if her attempt to ratify a divorce deal fails.

Speaking to the parliament on Tuesday, May said that if she fails to get an approval for her deal by March 12, then lawmakers would be given a vote on March 13 on leaving without a deal. 

If they reject that option, then lawmakers would have a vote on March 14 on a motion requesting a "short, limited extension" Brexit delay, she said, adding that any delay could only be until the end of June.

Read more: May postpones Brexit vote, EU mulls delay to 2021

"Let me be clear, I do not want to see Article 50 extended. Our absolute focus should be on working to get a deal and leaving on March 29," she told the parliament.

"I believe that, if we have to, we will ultimately make a success of no deal," she added.

May's comments opened up the possibility of taking a no-deal off the table, marking one of the biggest turning points in the UK's labyrinthine Brexit crisis since the shock 2016 referendum vote to leave the EU.

May is still negotiating changes the parliament has demanded, according to her, the EU has accepted desire to work on backstop alternatives instead of rejecting them. She pledged to put any changes agreed with the EU before the parliament ahead of vote.

Labour: 'May's Brexit deal should face public vote'

In response to May's remarks, UK Opposition Labour Party leader Jeremy Corbyn called May's approach "grotesquely reckless."

The party spokesperson Keir Starmer said earlier Monday that it would back calls for a second referendum on Brexit if the parliament rejects May's alternative plan for leaving the EU.

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Starmer said the second vote would be between remaining in the EU and the option of a "credible leave deal," one that had the parliament's backing.

"If the prime minister's deal gets through, that deal should be subject to the lock, if you like, of a public vote," Starmer stressed.

After the British parliament voted 432-202 against her deal in January, the worst defeat for a government in modern British history, May is making a last-ditch effort to get concessions out of the EU.

But many British lawmakers and some of her own ministers have warned they will try to take steps to avoid thrusting the world's fifth largest economy into a potentially tumultuous economic crisis.

Britain is due to leave the EU on March 29.

How Wednesday's parliamentary Brexit debate will work

Lawmakers on Wednesday will debate a simple government statement which reads: “This House notes the Prime Minister's statement on EU exit of 26 February 2019; and further notes that discussions between the UK and the EU are ongoing.”

Lawmakers can propose a change to the wording. They are known as amendments and, if approved by a vote, could exert political pressure on May to change the course of Brexit. However, the government is not legally bound to follow any changes approved following the debate.

Parliament Speaker John Bercow chooses which amendments are selected for debate.

Speaker Bercow will decide whether to select any of the amendments for a vote at the start of the debate, due around 1 p.m GMT.

Lawmakers will vote on each of the selected amendments one by one, before voting to give final approval to the wording of the motion itself. Voting is due to begin at 7 p.m GMT. Each vote takes around 15 minutes, and the result is read out in parliament.

(Cover: British Prime Minister Theresa May during a  press conference at the Arab-European Summit in Sharm El-Sheikh, Egypt, February 25, 2019. /VCG Photo)