Those surveyed by Sky News found that the choice to Remain was the preferred option - with 48% supporting staying in the European Union compared to 27% preferring a "no-deal" Brexit and just 13% supporting the Chequers agreement.
The PM's spokesman reiterated today that there would "be no second referendum in any circumstance" following the publication of a poll showing that a majority now back a People's Vote on the final Brexit deal by 50% to 40%.
Brexit negotiations are high on the agenda Tuesday for Hunt, who later heads to Austria to convince European counterparts to engage with British proposals for a deal.
May has repeatedly ruled out holding another public vote on Brexit, saying the public spoke at a June 23, 2016, referendum, in which 51.9 percent of the votes cast backed leaving the European Union while 48.1 percent backed staying.
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Mr Mundell said he could not accept a Brexit deal that "threatens the integrity of the United Kingdom", including any "backstop" plan to prevent a hard border in Ireland that creates a new customs frontier in the Irish Sea. Speaking at a rally in early July, he promised to "liberate the people from this Europe", urging voters to turn the 2019 European Parliament elections into a "referendum between the elite, the banks, finance, immigration and job security, and the Europe of the people and of work".
However, the potential for major political upheaval remains, with May's minority government facing a series of make-or-break moments in the Brexit process over coming months. Failure at any of those three hurdles could cost her her job.
Remarking that since the Chequers deal, May had come to embrace a very different approach to negotiations which Brexiteers have found increasingly unacceptable, Mandelson told Sky anchor Adam Boulton that "she has deserted her previous approach, she wants to find a new approach to the Brexit negotiations, and she has crossed the Rubicon but leaving a very large number of Tory MPs on the other bank".
The proportion of Britons satisfied with May's performance dropped to 24 percent, down by 17 percent since March, the Sky poll showed. The Sky poll said 65 percent of British voters thought the government would end up with a bad deal, up by 15 points from March. Just 10pc thought the government was doing a good job.