U.K. Prime Minister Theresa May has offered lawmakers a vote on whether to have a second Brexit referendum if they approve her withdrawal agreement.

Addressing reporters on Tuesday, May outlined her new Brexit proposals which are being voted on by politicians next month. Her previous agreement has been rejected three times by U.K. lawmakers.

Detailing her new deal, she said that the government would include a requirement to vote on whether to hold a second Brexit referendum. May's new proposal is seen as a last-ditch attempt to get her Brexit deal through Parliament, and the promise of a vote on a referendum could sway many pro-Remain politicians to back her deal.

"For those MPs who want to a second referendum to confirm the deal, you need a deal and therefore a withdrawal agreement bill to make it happen," May said Tuesday.

"This (vote) must take place before the Withdrawal Agreement can be ratified," May told reporters.

"And if the House of Commons were to vote for a referendum, it would be requiring the government to make provisions for such a referendum including legislation if it wanted to ratify the Withdrawal Agreement."

Sterling had initially jumped Tuesday afternoon following a report that May will allow lawmakers a free vote on a second Brexit referendum. A free vote would mean politicians could choose their own preferred option — and not be "whipped" into a decision by party chiefs — potentially improving the chances of another Brexit referendum as lawmakers in the U.K. Parliament are largely pro-remain.

The Bloomberg report, citing sources, said that May had proposed the idea to her senior politicians, sparking a backlash from pro-Brexit ministers in her cabinet.

The pound jumped 0.7% to $1.2815 from $1.2725, its highest since Friday, according to Reuters, before giving up some of those gains. By 4.40 p.m. London time, sterling was trading at around $1.276.

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