Some 2.6 million voters who backed Leave in 2016 have switched to the Remain side, supporters of a referendum on the terms of Brexit have claimed.
But, according to analysis for the Best for Britain campaign, another 1 million former Remain voters have moved in the opposite direction and now back Brexit.
The findings suggest an overall shift of 1.6 million voters in favour of continued EU membership - enough to overturn the 2016 referendum in a new poll.
Best for Britain and Hope not Hate commissioned analysis of two YouGov polls involving a total of more than 15,000 people, taken before and after the release of Theresa May's Chequers plan for Brexit.
The results from data company Focaldata suggested that there has been a shift towards Remain in 93% of the 632 constituencies in England, Scotland and Wales covered by the research, with 112 seats switching from majority Leave to Remain. Some 341 seats in Britain now have a majority to stay within the EU against 291 wanting to Leave, according to the analysis.
In a finding likely to put additional pressure on Jeremy Corbyn to give his backing to an EU referendum, the analysis suggested that 1.4 million of those switching to Remain voted Labour in the 2017 general election.
The largest group of pro-Remain switchers were young women who voted Conservative in 2015, Leave in the referendum and Labour in 2017.
And some 63% of new voters said they would back EU membership in a second poll.
Labour MP David Lammy, a prominent supporter of Best for Britain, said: "After two years of stalling negotiations, job losses and skills shortages in the NHS, millions more voters have seen through the lies of Brexit.
"With the Tory government in the pocket of its hard right fringes, it's up to Labour to give these voters a voice.
"Labour members, Labour voters and many Labour MPs remain strongly pro-European. Our leadership needs to wake up and smell the coffee, by supporting a people's vote on the final deal."
Best for Britain chief executive Eloise Todd said: "This data shows the tide is turning on Brexit. People want to have the final say on whether we leave Europe or not."
The research was released as Best for Britain launched a £200,000 publicity campaign calling for an "emergency stop button" to halt Brexit.