Findings will bolster those in No 10 who want to negotiate on re-entry but some senior figures remain wary

Andy Burnham’s personal preference to rejoin the European Union after the next election is supported by almost half of all voters, a new megapoll has found, although cabinet ministers concerned about reopening Brexit divides are privately urging him to proceed with caution.

The poll by the Messina Group (TMG) found that renegotiating the UK’s relationship with the EU could boost Labour’s vote share by as much as seven points, if the prime minister offered a fresh referendum in which he campaigned to re-enter the bloc.

Almost 1/3 of voters said an in-out referendum would be needed first, while more than one in six felt that a general election mandate would be sufficient, and the same proportion thought parliament could make the decision.

The overall findings will bolster the case of those inside Downing Street who want to promise at the next election that Labour would at least negotiate over re-entry, which the prime minister has said he wants to see “in his lifetime”.