Some 52% of 101,772 people quizzed online by the Mirror’s parent company, Reach, believe the public should be given a say on whether “they support a final deal on Brexit”.
And 49% of people think a second referendum should include an option to Remain in the EU, with 37% against.
Fuelling calls for a poll re-run, 55% of people claim they did not have enough information to make an informed decision in the 2016 vote.
Only 28% disagreed.
If a new referendum was held tomorrow, 50% would opt to stay, with just 32% backing Brexit, according to the findings of the study run with Google Surveys.
The other 18% either don’t know or wouldn’t vote.
Meanwhile, 45% of those who answered think warring Westminster parties should form a government of national unity “to ensure Brexit is delivered smoothly”, with 29% against.
Just a fifth of those who responded said Labour’s position on Brexit was clear, with exactly half disagreeing.
Regional breakdowns show support for a second referendum was highest in Merseyside, where 60% of respondents backed another poll.
Opposition to a fresh vote was highest in Grimsby, where 37% disagreed with the statement: “UK voters should be allowed to vote on whether they support a final deal on Brexit”.
If another referendum was held tomorrow, the majority for Remain would be biggest in Merseyside and Greater Manchester, with 57% backing staying in the bloc.
The highest majority for Leave would be in Grimsby and Lincolnshire, with 43% backing quitting the EU.
Labour MP Ian Murray, of the Best for Britain campaign, said: “This major survey confirms that the British people want their say on the final Brexit deal.
“With the government in absolute chaos and Theresa May forced into a humiliating retreat, it is now time to put this issue back into voters’ hands.
“The lies and misinformation from the 2016 referendum have been exposed, and the majority of people now want to remain in the EU.
“No matter what the Prime Minister tries to achieve in Brussels, the best deal is the one we currently have as a member of the EU with our UK opt-outs – which it was confirmed yesterday that we can keep.
“Theresa May must recognise the results of this survey and put this to a ‘people’s vote’.”