Jeremy Corbyn has accused May of a "cynical" attempt to run down the clock before the March 29 Brexit date in order to leave MPs with a stark choice of accepting her deal or crashing out of the European Union without any agreement.
The PM has promised another "meaningful vote" in the coming weeks, but Labour is determined to reduce her wriggle room.
Last month, Parliament voted in favour of an amendment that supported most of the PM's deal but called for backstop - which is a last-resort option to prevent a hard border in Ireland - to be replaced with "alternative arrangements".
The opposition accuses May of wanting to force MPs to make an all-or-nothing vote between her deal and a chaotic Brexit shortly before Britain is set to leave the European Union on March 29. 'There needs to be a day when Parliament says that's it, enough is enough'.
British Prime Minister Theresa May will pledge this week to give parliament another chance to voice their opinions on Brexit by February 27 as she tries to buy more time to negotiate a new deal with the European Union.
"It's this blinkered approach that's got us to where we are, with her never wanting to see where the real majority is in parliament".
DIT says that with the agreement the British auto industry, which has consistently warned against a no-deal Brexit, could avoid up to £8m a year in tariff charges on their exports that would apply if the agreement had not been reached.
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Instead he appeared to be trying to outflank Mrs May by pitching to join forces with Tories who want a softer Brexit.
In a speech in Coventry he said Labour's plan "could win the support of Parliament and bring the country together" but Mrs May has so far "chosen the path of division".
On Thursday - Valentine's Day - MPs will consider a motion on Brexit and a series of amendments, likely to include shadow Brexit secretary Sir Keir Starmer's attempt to impose a new deadline for a vote on the deal.
Mr Corbyn said that without an election "we will keep all options on the table - as agreed in our conference motion - including the option of a public vote".
Deputy Labour leader Tom Watson told the Andrew Marr Show that if those conditions were not met then his party could move to supporting a second referendum.
In a letter to Labour leader Jeremy Corbyn dated Sunday, May opposed his party's appeal for the country to remain in a customs union with Brussels.
"I'm certain of one thing, is that it's not going to be as good as if they had not been Brexit, that is for sure", Lagarde said.