Jeremy Corbyn is facing demands to hand power over Labour Brexit policy to members, by holding an emergency conference on endorsing a second referendum.

The grassroots call comes as Roberta Blackman-Woods, a shadow communities minister, on Saturdayjoined other party frontbenchers in backing a people’s vote if – as is highly likely – Theresa May’s proposed Brexit deal is rejected by MPs.

“I can certainly say that if we vote down the deal in parliament then I think it is really important that we have a people’s vote,” she told the Our Future Our Choice group, a youth campaign for a second vote.

She spoke out after Steve Reed, a shadow culture minister, said last week that “only the people can break the logjam”, as he diverged from the party’s official line. Many more frontbenchers are poised to support a second referendum on Britain’s exit terms if May’s draft deal is defeated in the Commons.

It has now emerged that some members are preparing to demand a special party conference. A motion, seen by the Observer, is being circulated among constituency parties and Labour’s affiliated groups. It says that “the UK is facing a national crisis and the future of our country is at stake”.

The only item on the meeting’s agenda would be the motion: “This conference believes that the citizens of the UK must have the final say through a people’s vote on the deal proposed by the government for leaving the European Union, with an option to remain in the EU on the ballot paper.

“This conference calls on all members and our elected representatives to campaign for a people’s vote with urgency and vigour.”

While the grassroots back Corbyn’s leadership, the membership is also heavily in favour of a new vote. Those interested in a special conference want to try to stop it being seen as an attempt to undermine Corbyn, by setting out clearly that it would be called only to endorse another referendum.

Roberta Blackman-Woods. Photograph: Stuart Forster/Rex

The last special conference was held under Ed Miliband in 2014 to approve changes in the party’s leadership election rules. Such an event can be held at just 10 days’ notice. All delegates at this year’s Liverpool conference would have the right to attend.

Those delegates overwhelmingly backed a policy that ensured a second vote remained an option should it prove impossible to secure a general election. Labour policy is to fight for an election before other options, such as a new poll, are supported. The party could secure an election should it gain a majority in the Commons for a vote of no confidence in the government. That still seems unlikely, although support for May is waning among the Democratic Unionist party, which is threatening to pull the plug on its support for her minority government.

Disagreements within Labour are as bitter as ever, with some MPs accusing shadow cabinet members of being bigger supporters of Brexit than Tory Brexiters. However, the party leadership believes Labour must be seen to respect the referendum result.

“In the parliamentary party, there’s a group who want a second referendum now, but there is another group – including frontbenchers – who think they can only get behind that publicly after May’s deal has collapsed,” said one shadow minister. “That group is substantial. They can’t shout for it now, but they can once May’s deal has been voted down by parliament. No proposal can command support, so it should go back to the people.”

Christina Rees, the shadow Welsh secretary, told a local party meeting last week: “Part of me hopes we never come out, but that’s just a personal issue.” But she added that she accepted the referendum result and defended the party’s current stance.

A YouGov poll for the People’s Vote campaign has found that 66% of voters believe Labour’s Brexit policy is unclear. However, 63% of those asked also thought the Tory position was unclear. It found that 62% of Labour voters said there should be a second vote if May’s Brexit deal was blocked by the Commons.

Many Labour MPs are looking for signs of a change of heart by Corbyn. Many were impressed by his performance in the Commons last week, when he dismissed May’s deal as the “blindfold Brexit we all feared”.

Others, however, were disheartened by an interview in which he said he did not know how he would vote if there were a second referendum because he did not know what options would be on offer.