Just 23 per cent said they would back the Prime Minister’s deal. That’s compared to 57 per cent who said they would support leaving the EU without an agreement.
A two-way referendum would see 29 per cent of Tory members endorse Mrs May’s stance, with 64 per cent suggesting they would vote for a no-deal scenario, according to the poll.
The YouGov poll funded by Economic and Social Research Council comes at a crucial time for the Prime Minister as she faces a crunch vote on her plans in the Commons.
After she suddenly pulled a vote on the Withdrawal Agreement in December because it faced a significant defeat, MPs are to begin debating the proposals again next Wednesday.
The vote is scheduled for the following week.
The poll findings also came as Mrs May’s Brexit agenda was hit by a series of blows.
DUP deputy leader Nigel Dodds insisted his party’s opposition to Irish border backstop proposals had not lessened after a meeting with the Prime Minister on Thursday.
Mr Dodds said: “The Withdrawal Agreement, as currently proposed, flies in the face of the Government’s commitments on Northern Ireland as we leave the EU.”
However, Irish Taoiseach Leo Varadkar insisted there could be no changes to the backstop, which is intended to prevent a hard border in Ireland by ensuring the UK abides by EU customs rules if no trade deal is agreed by the end of a Brexit transition period.
Mr Varadkar said he had spoken to German chancellor Angela Merkel by telephone on Thursday and the two leaders agreed to “stand by” the Brexit deal.
He said: “We’re happy to offer reassurances and guarantees to the UK, but not reassurances and guarantees that contradict or change what was agreed back in November.”
And as the EU closed ranks, the European Commission confirmed “no further meetings are foreseen” with the UK on updating Mrs May’s Brexit deal because negotiations have concluded.
Mrs May is pressing European leaders for more flexibility on the Irish backstop as a way of garnering more backbench support for her exit plans.
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