Labour activists who want to ditch Brexit because they believe it will make it impossible for the party to implement a leftwing manifesto have launched a fresh campaign for a second referendum.

The move puts Jeremy Corbyn under increasing pressure to drop his resistance to a new public vote.

A “model motion” stating that Labour should campaign to put the issue to the people again and then back Remain is being circulated to all constituency Labour parties by Corbyn supporters. They hope most local parties will sign up to it before Theresa May returns her Brexit deal to the House of Commons some time next month.

The campaign is being run by young leftwing Labour activists headed by Michael Chessum, a former member of the steering committee of the pro-Corbyn grassroots movement Momentum. He now heads the group Another Europe Is Possible, which helped shift party policy in the direction of a second referendum at its annual conference in Liverpool in September.

Chessum said activists in all constituency Labour parties were being contacted by phone to urge them to back the motion, which he believes could be supported by more than 100 local parties by the middle of January.

The motion says: “The Tories’ Brexit agenda will deregulate and destabilise the economy, attack our rights and freedoms, and undermine our ability to implement a radical manifesto.

“We welcome the call of conference to put a public vote firmly on the table as a means of stopping this agenda, not because we are fanatics for referendums, but because we need to stop the process by which Tory free-marketeers are driving British society off a cliff. Any public vote on Brexit must, to be meaningful, include an option to Remain.”

It adds that “Labour must campaign for a public vote on Brexit with an option to Remain, and include such a vote in our manifesto”.

The move exposes the deepening tensions within Labour, and reflects intense pressure being applied from parts of the Corbyn-supporting mass membership on the leader.

Jeremy Corbyn strolling to the gym near his north London home. Photograph: Noble/Draper

Party members and supporters overwhelmingly oppose Brexit and a clear majority back a second referendum while Corbyn, a lifelong Eurosceptic, and some of his allies are resistant, believing a second referendum could lead to a huge loss of traditional party supporters to Ukip.

The divisions over a new public vote are also deep within the shadow cabinet. The Observer has been told that at last week’s meeting, Ian Lavery, the party chair and joint campaign co-ordinator, said he was convinced that if Labour backed a second referendum it would be severely punished by Leave supporters who would desert in droves.

“Lavery said: ‘I promise you that if we back a second referendum we will lose the next general election,’” said a source at the meeting.

After Rosena Allin-Khan, the Labour MP for Tooting, came out in support of another public vote last weekend she received a letter from Corbyn’s office reminding her in no uncertain terms that Labour was still not committed to the policy and that its position was to fight for a general election, not back another referendum.

Members of the shadow cabinet also remain undecided this weekend about the best time to force a confidence vote in the government to try to force an election – despite May suffering repeated humiliations over Brexit.

A group including Lavery fear that if they call a vote and fail to force a general election they will not only have united the Tories, but will then themselves come under greater pressure to back a second referendum. The party’s Brexit spokesman, Keir Starmer, is understood to be less resistant, believing that Labour must find a moment soon to call the vote and then, if it loses, be ready to back a second referendum.

The latest Opinium poll for the Observer, taken after May survived a confidence vote on Wednesday among her own MPs, despite 117 Tory MPs failing to back her, shows Labour’s lead over the Conservatives has dropped from three points a month ago to just one point, despite the crisis engulfing the government.

Labour is unchanged on 39%, while the Tories are up two points to 38%. The Liberal Democrats have gained one point to stand on 8%, while Ukip has dropped by two points to 6%.

While approval for the prime minister over her handling of Brexit is low, it is virtually unchanged since a month ago, while Corbyn’s approval rating on Brexit has dropped and is below that of May’s. The survey found 53% of UK adults disapprove of May’s handling of Brexit against 28% who approve. But only 16% of UK adults approve of Corbyn’s handling of Brexit, against 55% who disapprove. Last month 19% approved and 50% disapproved.

When asked whether, in the event that May’s deal is voted down by parliament, there should then be another public vote, 46% of UK adults said they thought there should definitely or probably be one, against 40% who thought there probably or definitely should not be.

Among Labour supporters 65% favour the idea of a second referendum against 21% who oppose it. Among Tory supporters 31% back the idea against 60% who oppose it.

Meanwhile, a group of senior Conservatives is urging colleagues to “rebuild support with younger voters” by backing a second referendum.

Former deputy prime minister Lord Heseltine, Dominic Grieve MP and Lord Willetts are among the Tory MPs and peers who have written a joint statement saying that if their party does not back another referendum it risks “losing young people for good”.

“If we are to remain a party of government, it is absolutely critical that we increase our support among younger generations,” they say.

“To do this, we must listen to and engage with their concerns on Brexit. They voted overwhelmingly to Remain in the European Union in 2016 – and since then have become even stronger in their views. Since the referendum, nearly 2 million young people are now of voting age. Of those in this group who are certain to vote, an astounding 87% support the United Kingdom staying in the European Union. If we do not hear their voices, who could blame them for feeling excluded and powerless on this most vital issue. The truth is that if Brexit fails this generation, we risk losing young people for good. Our party’s electoral future will be irrevocably blighted.”