The huge study carried out by YouGov, which surveyed a weighted sample of more than 10,000 people, found just a quarter want parliament to be given the final decision.
The key finding comes as concern over a no-deal Brexit increases, precipitating a slump in sterling amid news that the UK government is stockpiling food and medicine.
The findings are also a major boost to the People’s Vote campaign for a new referendum, which commissioned the poll, and The Independent’s own Final Say campaign – which has attracted more than half a million signatories to its petition.
The survey also shines a light on views of Brexit’s progress, with large majorities thinking talks are going poorly, that the process of leaving has been a mess, that the country would end up with a bad deal and that the British government would bear responsibility.
Former president of YouGov Peter Kellner said: “If the Brexit negotiations with Brussels break down, a two to one majority of voters want the public, not parliament, to decide what happens.
“Even people who voted Leave tend to prefer a new referendum, by 39-34 per cent. This is politically significant.
“There is clearly the potential for a broadly based campaign this autumn for a people’s vote should the Brussels talks go badly. Support for a new referendum would go well beyond the ranks of those who want to stop Brexit.”
The pollsters asked “should the final decision be made by MPs voting in parliament or the public voting in a new referendum”, if the UK had to choose whether to remain in the EU or leave with no deal.
Half, 50 per cent, said the decision should be given to the public voting in a new referendum. Just 25 per cent said parliament should decide and 25 per cent said they did not know.
Asked whether people agreed with the statement that “the negotiations are going badly at the moment”, a huge 74 per cent agreed to some extent, with just nine per cent disagreeing and 17 per cent saying they did not know.
An even larger 83 per cent agreed with the statement that the “process of leaving the EU so far has been a mess”, with just six per cent disagreeing and ten per cent saying they did not know.
Labour MP Chuka Umunna, a leading supporter of the People’s Vote campaign, said: “Whether people voted leave or remain two years ago, nobody voted for this chaotic Brexit that will damage our living standards and public services, and which is being thrust on the country by politicians in Westminster.
“It is now clear that the people are starting to find their voice, and they demand a vote on the final Brexit deal as the only way out of this mess.”
Some 68 per cent agreed that “problems in the negotiations with the EU make it likely that Britain will get a bad deal”, with 13 per cent disagreeing and 19 per cent saying they did not know.
In an ominous sign for the prime minister, 64 per cent agreed with the statement “if we get a bad deal, it will mainly be the UK government’s fault”, with 23 per cent disagreeing and 14 per cent saying they did not know.
In the case that negotiations are completed, 45 per cent backed a new referendum on the deal, while 34 per cent opposed it and 22 per cent said they did not know.
Asked how people would vote if there is a referendum today, 46 per cent said they would vote to remain, 40 per cent said they would vote to leave, six per cent said they would not vote and seven per cent said they did not know.
The Independent launched its Final Say campaign last month with a petition to demand a new referendum attracting hundreds of thousands of votes in a matter of hours.
Downward pressure on sterling continued amid a sell off on Thursday, with the pound down 0.24 per cent at $1.2854 after dipping below $1.29 for the first time in 12 months on Wednesday.
The currency was also slightly lower against the euro, at €1.1093, although it regained some ground lost in the previous session.
The threat of no-deal has also weighed heavily on the optimism of UK businesses, while key figures in the science community have said no-deal would be a disaster for the UK.
A spokesman from the Department for Exiting the European Union said: “The people of the United Kingdom have already had their say in one of the biggest democratic exercises this country has ever seen, and the prime minister has made it clear that there is not going to be a second referendum.
“We remain confident we will agree a mutually advantageous deal with the EU.”
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