Jeremy Corbyn has refused to back a second Brexit referendum despite a poll saying almost three quarters of Labour members want one. 

The party leader has come under renewed pressure to throw his weight behind a so-called “people’s vote” after a YouGov survey of more than 1,000 members found 72% support the move. 

But speaking at an event in London, Corbyn insisted MPs must first vote on Theresa May’s deal with Brussels before Labour considers its next move. 

The party’s policy, decided at a conference last year, is to keep a re-run of the vote on the table, but Corbyn stressed that “was very much after the votes have taken place” in Westminster. 

He said: “We haven’t yet had a vote [on May’s deal] and I think the government really should be ashamed of itself.

“This vote has been delayed and delayed and delayed. It’s finally going to take place the second week of January. That is not acceptable, this vote should have taken place more than a month ago. This government is just trying to run down the clock and create a sense of fear between either no deal or May’s deal.” 

He underlined Labour’s policy was to push ministers to seek a permanent customs union with the EU, adding: “What we will do is vote against having no deal, we’ll vote against Theresa May’s deal, at that point she should go back to Brussels and say this is not acceptable to Britain and renegotiate a customs union, form a customs union with the European Union to secure trade.”

Corbyn, who was a known Eurosceptic during his 36 years as a backbench MP, has previously said it is his priority to seek a general election and negotiate a new deal with Brussels. 

But with less than three months to go before the Article 50 deadline on March 29, resisting the views of his pro-remain membership will frustrate his supporters. 

The so-called meaningful vote on May’s deal is due to take place on January 15. 

Outside the membership, the study also found strong backing for a second vote among Labour supporters.

Some 57% of current Labour voters, and 61% of those who backed the party at the 2017 general election, want Corbyn to “fully support” a fresh referendum.

The study also suggests tens of thousands of Labour members could be prepared to quit the party over the leadership’s approach to Brexit.

The work was carried out by YouGov for the Economic and Social Research Council-funded Party Members Project.

Professor Tim Bale, of Queen Mary University London, said: “Our survey of Labour’s grassroots clearly shows that Corbyn’s apparent willingness to see the UK leave the EU – a stance he has recently reiterated – is seriously at odds with what the overwhelming majority of Labour’s members want, and it doesn’t reflect the views of most Labour voters either.”

Labour MP Phil Wilson is among those urging Corbyn to switch position.

He said: “An overwhelming majority of Labour’s voters, as well as its members, want the public to have the final say on Brexit and to stay in the European Union.

“But the leadership has too often hidden behind myths that Labour is almost evenly divided on this issue when the clear evidence from this and other polls shows that it is the leadership which is increasingly out of step with its supporters.

“I urge Jeremy to seize this chance to change the course of history, before it’s too late.”

YouGov surveyed 1,034 Labour members for the study, as well as a sample of 1,675 British adults.