British Prime Minister Theresa May said a vote on her Brexit deal will "definitely" happen next week, even as a new poll shows a majority of Britons would vote to remain in the European Union if there was a second referendum.

"We're going to be in uncharted territory if this deal does not go through," May warned in an interview with the BBC.

The British leader said that since the vote was pulled at the last minute in December, she's been consulting with EU leaders and British colleagues to get new assurances in three key areas, the details of which will be laid out in the coming days.

Those three areas include specific measures for Northern Ireland, a greater role for parliament in negotiations on the next stage of future U.K.-EU relations, and further assurances from the EU to address concerns over the Irish backstop.

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"When MPs come to look at this vote, they need to ask themselves: Does this deal deliver on the referendum? Yes, it does. Does it protect our jobs and security? Yes, it does. Does it provide certainty for businesses and citizens for the future? Yes, it does," May explained.

Under forceful questioning from the BBC, May said that there should not be a second referendum.

A new YouGov survey showed that if a second referendum were held now, 54 percent of British citizens would be in favor of remaining in the European Union. The poll, which was commissioned by People's Vote, an organization pushing for a new referendum, also found 41 percent thought the final decision about Brexit should be made by a new public vote rather than leaving it in lawmakers' hands.

A deal setting out the terms of the United Kingdom's divorce from the EU has been agreed to between the prime minister and the EU, but it must pass a vote in Britain's Parliament before it is formally adopted.

Lawmakers are expected to vote on it either January 14 or 15. The U.K. is due to leave the EU on March 29.

"Don't' let the search for the perfect become the enemy of the good," May said. "I want to see this deal go through."