In total, the Brexit Party would collect 24 per cent of the ballot, with the Conservatives trailing on just 22 per cent, it was found. Labour would win with 27 per cent of the electorate backing them.
Some 34 per cent of voters say they will back it on Thursday, Opinium found. That compares to just 20 per cent who say they will support Labour in second place and 15 per cent who indicate they would vote for the Lib Dems.
The Conservatives, in that poll, remain fourth – a finding that is expected to heighten despondency in the party and lead to renewed calls for Theresa May to set a definitive timetable for standing down as prime minister.
Change UK, meanwhile, a party formed with the express intention of forcing a second Brexit referendum, is struggling with just 3 per cent of voters saying they would back them in either ballot.
A hypothetical question asking who voters would support in the upcoming European election if Labour pledged to support a second referendum on Brexit found the party boosted its share to 30 per cent.
Adam Drummond, head of political polling at Opinium said: “While the home for dissatisfied leave voters was established quite early on as Nigel Farage’s Brexit Party, until recently Remainers dissatisfied with the major parties have struggled to unite around a single pro-remain party.
“However, with less than a week to go there are signs that the Liberal Democrats are emerging to fill this slot. Although their share of the Remainer vote (29 per cent) is nowhere near the 63 per cent share the Brexit Party has among Leavers, they have overtaken Labour (28 per cent).”
He added: “The question is whether that trend continues in the few days of campaigning left.”
The poll was carried out via an online survey of 2,004 UK adults between 14-16 May.