Labour has been considering how to head off a concerted attempt by remain-supporting members to stage a vote at its annual conference calling for a second referendum, to avoid what would be an embarrassing defeat for Jeremy Corbyn on the party’s Brexit policy.

About 130 constituency Labour parties (CLPs) were understood to have expressed willingness to back a motion in favour of a second vote, drafted by the pro-Corbyn campaign group Labour for People’s Vote.

To avoid a damaging defeat, one option is to invite delegates to support a Brexit policy statement that would refer to holding a second referendum, but only in exceptional circumstances.

It could be similar to a watered-down resolution that was supported at Unite’s policy conference in July, which was offered by the union leadership to defuse a similar situation.

Major new polling of 10,000 people suggested Labour voters backed a second referendum by 63%, with just 8% opposed, in one of the largest surveys of public opinion since the referendum to leave the European Union.

The research by the People’s Vote campaign, which supports a referendum on the final deal with the option to remain, suggested Labour voters would back staying in the EU by a margin of three to one if the poll was rerun.

The MP Chuka Umunna, a leading supporter of the campaign, said: “This poll shows that Labour voters overwhelmingly support a people’s vote, putting them at odds with the party’s official pro-Brexit position.”

Nine local parties have already formally submitted the motion for debate at the party’s conference in Liverpool but organisers hope to persuade as many as 300 constituency Labour parties to submit the motion – an unprecedented number.

The motion urges Corbyn to oppose a Tory Brexit deal and to “call for an immediate general election and make a manifesto commitment to call a public vote on the deal with an option to remain in the EU”, adding: “If we cannot get a general election, still campaign for a public vote, and call for a general election following a government defeat in that vote.”

A potential party split over Brexit at last year’s conference was halted by Momentum’s powerful caucus. Delegates were urged to pick other topics for debate, including housing and social care, omitting Brexit as a topic, in order to avert a vote on the single market or free movement that could embarrass the leadership.

Instead, conference delegates were invited to support the national executive committee policy statement on Brexit.

Campaigners suggested conditions would be more fertile for a compromise this September, compared with when Corbyn-sceptic MPs had led the drive.

Michael Chessum, one of the organisers behind the motion, said it was “overwhelmingly being led by people on the left of the party”.

“For us, the aim is not to defeat the leadership – quite the opposite, it’s to strengthen it and give it room to shift to a firmer position on Brexit,” he said. “Taking a position in favour of a people’s vote is Corbyn’s quickest and best route to power, as well as being the right thing to do.

“So we hope that, come conference, there will be a broad consensus, including the leadership, in favour of giving the people the final say. It’s a consensus that is already being formed at the grassroots of the party with the sheer number of CLPs passing motions in favour of it.”

Momentum’s position on Brexit has also shifted. A petition of its members calling for a second referendum was less than 300 votes away from the number it needed to force a vote of all members.

The Co-operative party, which is affiliated to Labour and shares 37 MPs with the main opposition party on a joint ticket, was expected at its annual conference in October to ask its delegates whether they would support a people’s vote.

A Labour spokesman said: “A second referendum is not our policy and we are not calling for one.”