Labour members are significantly more opposed to Brexit than Jeremy Corbyn is, with 72% of them thinking their leader should fully support a second referendum, according to a study of attitudes in the party.

The polling, part of an ongoing wider academic study into attitudes in various parties, found that only 18% opposed Labour campaigning for a second referendum, while 88% would then opt for remain if such a vote was held.

Official Labour policy is that a second referendum could potentially be considered if there is not a general election. However, Corbyn is publicly lukewarm on the idea, and prompted dismay among some party activists last month by saying he expected Brexit to happen even if Labour won a snap election.

Corbyn is facing intense pressure from some in the party to change course, with one pro-remain party group pushing for a motion that Labour would guarantee a referendum if there was a general election.

The study, part of the Party Members Project led by Prof Tim Bale of Queen Mary University of London, found that while Labour members still strongly supported their leader overall, they appear both distanced from his views on Brexit and, for some, sceptical about his motives on the subject.

The polling of 1,034 party members shortly before Christmas found that almost two-thirds believed Corbyn was doing very well or fairly well as leader, and 58% believe he could get a better Brexit deal than Theresa May as prime minister.

But asked why they felt Corbyn had not campaigned for a second referendum, 23% of those asked said it was because the Labour leader backed leaving the EU. Another 34% put the decision down to not wanting to alienate Labour voters.

If a new referendum was held, 88% of members would back remain, both in a two-way vote against either May’s plan or no deal, or in a three-way poll between all of them.

The findings “increase the pressure on Labour’s leader to get off the fence”, Bale said. “If Jeremy Corbyn genuinely believes, as he has repeatedly claimed, that the Labour party’s policy should reflect the wishes of its members rather than just its leaders, then he arguably has a funny way of showing it – at least when it comes to Brexit,” he said.

There was, he noted, some difference between the views of Labour voters and members. While a parallel poll of 1,675 voters found 73% of the party’s supporters believed the Brexit decision was a mistake, for members that rises to 89%.

On the impact of a no-deal departure, 89% of members said this would harm the economy in the medium to long term, against 65% of current Labour voters and 45% of all voters.

Of the near-third of members who said they oppose Labour’s current Brexit policy, 56% said the issue could make them quit the party – a potential loss of 88,000 people.

Bale said Corbyn “does need to think carefully about whether his ambiguity on the issue is quite as cunningly clever as many commentators seem to believe”.

He added: “It is because, if Corbyn carries on like this, then Labour risks losing some of the members on whom it’s relying to give it the activist edge over the Conservatives at the next general election.”

A Labour spokesman said: “As unanimously agreed at Labour party conference, if Theresa May’s botched Brexit deal is voted down in parliament then a general election should be called. In line with the policy agreed at conference, if the Conservatives block a general election then we will keep all options on the table, including the option of campaigning for a public vote.”