Amid raucous scenes in the House of Commons, May insisted that the deal she had secured with the European Union (EU) was still the best option on the table as she urged parliamentarians to get behind it.
Earlier, Opposition Labour Party had threatened to force a confidence vote in the government if May did not set a date for the vote, which was to be held last week but was postponed amid ongoing turmoil over aspects unacceptable to nearly all sides of the Commons.
In a parliamentary statement on Monday, May said lawmakers would resume the debate on her Brexit deal which was halted last week in the week of January 7, with a "meaningful vote" on the Withdrawal Agreement with the EU taking place the following week.
"When we have the vote, members will need to reflect carefully on what is in the best interests of our country," she said, stressing that she had won significant assurances from EU leaders over the contentious Irish "backstop".
Addressing critics who fear the clause is intended to leave the UK tied to EU rules beyond Brexit, May said she had been assured by the remaining 27 member-states that the Irish backstop was "not a plot to trap the UK".
The British premier, who remains firmly opposed to calls for a so-called People's Vote to give the public another say on Brexit, said such a repeat referendum would do "irreparable damage to the integrity" of the country's political system.
She said: "Let us not break faith with the British people by trying to stage another referendum. Another vote which would likely leave us no further forward than the last. And another vote which would further divide our country at the very moment we should be working to unite it."
Labour Party leader Jeremy Corbyn said May had "led the country into a national crisis" and no longer had Cabinet backing as he demanded an earlier vote on the Brexit deal.
"The deal is unchanged and is not going to change. The House must get on with the vote and move to consider the realistic alternatives," he said.
The UK voted to leave the EU in a referendum in June 2016 and the formal exit from the economic bloc on Brexit Day March 29, 2019 requires a deal cleared by its Parliament that sets out the terms of the exit and includes a declaration on the outline of the future relations between the UK and the EU.
However, without the Parliament's backing for the current deal, there are growing fears of a so-called no-deal Brexit.
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