Labour leader Jeremy Corbyn said his party would support a move that would give the British public a chance to vote on Theresa May’s Brexit deal if Labour’s proposals were rejected by Parliament later this week.He said the Labour Party leadership had taken the decision because of the Prime Minister’s failure to secure parliamentary support for her plan, leaving Britain on the verge of crashing out of the European Union without a deal on March 29. The British public voted in June 2016 to leave the EU.According to a statement, the Labour Party will put forward or support “an amendment in favor of a public vote to prevent a damaging Tory Brexit being forced on the country.””One way or another, we will do everything in our power to prevent No Deal and oppose a damaging Tory Brexit based on Theresa May’s overwhelmingly rejected deal,” Corbyn will tell a meeting of Labour lawmakers, according to the statement.May’s Conservative Party lambasted the Labour move, saying it wants “to betray the will of the British people & ignore the biggest democratic vote in our nation’s history.””Labour have ripped up their promise and are now pursuing a divisive 2nd referendum that would take us back to square one,” the Conservatives tweeted.Labour said it will set out five demands in Parliament this week, including a permanent customs union with the EU and “close alignment” with the bloc’s single market.It added that it would support a cross-party amendment — known as the Cooper-Letwin amendment — that aims to rule out a no-deal outcome by extending Article 50 and delaying Brexit.If rejected, the party will then support a public vote, Labour’s Brexit spokesman Keir Starmer tweeted.”This week Labour will put its alternative plan for a vote in the House of Commons,” Starmer wrote. “If Parliament rejects our plan, then Labour will deliver on the promise we made at our annual conference and support a public vote.”A Labour Party press officer told CNN that there are still no details of what form the public vote would take or when it might take place.May under increased pressure to delay BrexitMay has come under increased pressure in recent weeks to delay leaving the EU on March 29.Parliament was due to vote on her beleaguered deal Wednesday, but it was again delayed by the Prime Minister in a desperate effort to buy more time. May’s party is splintering over her handling of Brexit.Speaking to reporters on Sunday, May said the vote would now happen by March 12 — a mere 17 days before Brexit day. The Prime Minister is due to update lawmakers on negotiations Tuesday after she returns from talks with EU leaders in Egypt.British lawmakers overwhelmingly rejected May’s deal in January, which was agreed upon by the British government and the EU. The Northern Ireland backstop — an insurance policy designed to avoid a hard border between Northern Ireland, which remains part of the UK, and the Republic of Ireland, an EU member — has been a particularly thorny issue for May, with British politicians firm that they will not back her deal without changes.Meanwhile, the EU has reiterated that the deal cannot be renegotiated.CNN’s Kieron Michandani contributed to this story.