Grassroots Labour activists are preparing to step up their campaign to urge the party’s leadership to throw its weight behind a second Brexit referendum in the new year.

Jeremy Corbyn exasperated some supporters earlier this month when he reiterated Labour’s policy of seeking to renegotiate Brexit, rather than pushing for a fresh poll, if Theresa May’s deal is voted down next month.

The leftwing pro-remain group Another Europe Is Possible has been running phone banks to persuade local party members to pass a motion opposing Brexit and urging Labour to include a referendum in its manifesto if there is a general election.

“Any public vote on Brexit must, to be meaningful, include an option to remain. Labour should campaign for such a vote – and to remain,” it says.

The group, which helped coordinate grassroots activity in the run-up to Labour’s annual conference in September, believes half of local constituency Labour parties (CLPs) will have adopted the motion by the end of January.

There is no formal process for CLPs to influence Labour’s approach outside of conference time, but campaigners hope by bombarding the ruling national executive committee (NEC), they can send a clear message about party members’ views.

Michael Chessum, national organiser for Another Europe Is Possible, said the group would also support calls for a special Labour conference to weigh up Brexit policy.

“At every level of the parliamentary party, Labour seems to be divided on Brexit. What we need running alongside the debate is democracy, and the opportunity for members – who are overwhelmingly anti-Brexit and in favour of a fresh referendum – to set policy,” he said.

Separately, more than 250 members have signed an open letter to the NEC, organised by Gerard Burke of Milton Keynes CLP, calling for a special conference. More than 2,500 signed a petition over Christmas making the same demand.

The letter, sent to Labour’s general secretary, Jennie Formby, and the NEC, says: “The situation has changed radically and quickly since party policy on Brexit was agreed at conference in September.”

It urges all Labour MPs “to support a public vote at the earliest opportunity and where necessary work to build cross-party support to achieve this objective”.

Meanwhile, another campaign group, Labour for a People’s Vote, will be urging members to contact their MPs directly, and encourage them to support a referendum if MPs reject the prime minister’s deal.

Mike Buckley, the chair of Labour for a People’s Vote, said: “May’s deal hasn’t got any better over the break. Labour members and voters overwhelmingly want the deal voted down and then for Labour to support a public vote on the deal versus remain. A new vote is the only way to break parliamentary deadlock, and is the only democratic way ahead.”

Downing Street hastily postponed holding a vote on the withdrawal agreement on 11 December, after the overwhelming scale of opposition to it in parliament became clear.

The prime minister then withstood a no-confidence vote on her leadership from her own MPs, and pledged to seek fresh reassurances from Brussels over the Irish backstop before holding a vote on the deal in mid-January.

Corbyn drew back from tabling a full-blown motion of no confidence in the government, but has not ruled out doing so in the new year – and has repeatedly accused the government of deliberately “running down the clock” towards Brexit next March, by delaying the vote.