Supporters of Jeremy Corbyn from the leftwing campaign group Momentum are piling pressure on the leadership this weekend to give members a debate and vote on Labour’s Brexit policy in a move that will further expose the party’s deep divisions over Europe.

Several prominent figures on the left have told the Observer that it will be unacceptable – and reminiscent of the worst elements of Tony Blair’s leadership – if policy is decided behind closed doors. They are demanding that Brexit is fully discussed and voted on by delegates at the Labour party conference in Liverpool in September. The gathering will take place before any vote by MPs in parliament on the outcome of negotiations between Theresa May and Brussels.

The calls for involvement of the mass membership come as the leadership faces growing pressure from Labour MPs, peers and members to take a more pro-EU, pro-single-market approach as the main political parties prepare for a series of crucial Commons votes on the EU withdrawal bill in less than three weeks.

A spokesman for Momentum said the organisation remained supportive of the leadership on Brexit. But, increasingly, elements within Momentum and the trade union movement are demanding the right to be heard on the most important policy issue of the day, in line with Corbyn’s repeated pledges to involve members at every turn. The Trades Union Congress is expected to intensify its demands for the party to back staying in the single market in the coming months.

Rida Vaquas, a former member of Momentum’s national coordinating group, said: “The left has always stood against stage-managed conferences from the days of Blair, where decisions of substance are made behind closed doors whilst party members are given no chances to have robust debates on the direction of our party.

“A Corbyn-led Labour party can only be strengthened by vigorous discussion among our own ranks, on our political differences as well as what unites us. How we approach Brexit is an issue of decisive importance and it is therefore only right it is debated at conference. Socialists can never succeed by dodging political questions, only by facing them head on.”

Michael Chessum, who was on Momentum’s first steering committee in 2016/17 and is now national organiser of the leftwing anti-Brexit group Another Europe is Possible, said: “Jeremy Corbyn and the rest of the Labour leadership are principled people.

“They have spent decades fighting for democracy in the party and against the idea that important decisions can be made in smoky backrooms by officials. So I’m confident that they will support the right of members to democratically debate issues as pivotal as Brexit and free movement. There should be a consensus around that.

“Labour isn’t negotiating this deal, and the closer we get to exit day, the clearer it gets that the Tories’ Brexit agenda is going to be a disaster for the rights, freedoms and prosperity of working-class people and the communities that Labour and the left are supposed to represent. It is urgent that we clearly place an alternative to Brexit on the table – one linked to a radical vision for society under a Corbyn-led Labour government.”

Michael Chessum, national organiser of the anti-Brexit group Another Europe is Possible: ‘It is urgent that we clearly place an alternative to Brexit on the table.’ Photograph: Graeme Robertson/The Guardian

At last year’s Labour conference in Brighton, Momentum and some of the unions joined forces to prevent the Brexit issue being debated in order to avoid exposing the party split and embarrassing the relatively Eurosceptic Corbyn. At the time, many of his MPs and peers were pushing for him to back permanent membership of the single market.

This year the arguments over Brexit look likely to be even more heated and calls for a debate will be far more difficult to resist in September, when the date of the UK’s departure will be less than six months away.

Another Momentum member, Omar Raii, who sits on the London Young Labour committee and is a former NUS national executive committee member, said: “On an issue as big as this it would be unacceptable if we decided to determine our policy behind closed doors. It would be the worst kind of Blairite approach.

“It’s hugely important that Labour members democratically thrash out policy at conference on all issues, especially one as huge as Brexit. I hope to see Labour articulate a genuinely internationalist policy that opposes the reactionary, anti-migrant plans the Tories have for us.”

At a recent conference of the centre-left grouping Progess, nine candidates for Labour’s national executive committee launched the campaign LabourSay.EU to push for a meaningful vote on Brexit at the Labour conference.

Earlier this month, student unions representing almost 1 million young people studying at UK colleges and universities signed a statement calling for a “people’s vote” or second referendum on the final deal negotiated by May.