Multiple Labour MPs in Leave constituencies are pressuring Jeremy Corbyn not to whip on the vote for a second Brexit referendum.

Corbyn announced on Monday that Labour would back a second referendum if the party’s own Brexit deal outline is voted down. Labour MPs in Leave-supporting seats are now calling for a free vote on that second referendum proposal, to allow them to vote whichever way they want rather than follow a party line.

Kevin Barron, MP for Rother Valley and one of three Labour rebels who voted for Theresa May’s deal, said that “it is is clear that there is a huge dispute within Labour on whether we should have a second referendum, therefore we should have a free vote.”

An MP in a Leave seat said there had been a lot of backlash in her constituency following Monday’s announcement. “It was quite a shock when it came. We said in our manifesto that we were going to deliver Brexit while retaining the benefits of the single market and customs union, and now it feels like we’ve gone down a completely different path. A free vote would be within my interests,” she said.

Another MP in a Leave seat said he would struggle to vote for another referendum. “I honestly can’t understand the confidence of the ardent remainers as to winning such as vote, and with the current government in charge I shudder to think what options would be put to the public to vote on.”

A third MP in a Leave seat predicted that there would either be a free vote, or shadow ministers would be allowed to vote against the whip and keep their posts. “[A free vote] will probably happen as the leader can’t afford to lose more frontbenchers, although people got away with it last time and didn’t have to resign. I think discipline has broken down anyway so I’m not sure it matters—people will do what they need to do.”

Last month, eight shadow ministers abstained on an amendment by Yvette Cooper to delay Brexit so as to prevent no-deal, even though the Labour leadership whipped in favour of it. They were Gloria De Piero, Melanie Onn, Tracy Brabin, Judith Cummins, Yvonne Fovargue, Mike Kane, Emma Lewell-Buck and Jim McMahon.

A ninth shadow minister Julie Cooper, who is the MP for Burnley, wrote in her local paper the Burnley Express this morning that she has “no intention of voting for a second referendum”.

Caroline Flint, MP for Don Valley, called for a free vote in a tweet on Monday, saying that she would not support a second referendum and warning that Labour was in danger of overturning a manifesto promise. Gareth Snell, MP for Stoke-on-Trent Central, told Corbyn in the Commons yesterday that he “cannot vote for a second referendum no matter how much lipstick is put on it”.

Lisa Nandy, MP for Wigan, criticised the decision to back a referendum in the Guardian yesterday and said that though it might “help the party through a difficult week” it would cause many more problems in the long-term.

The amendment for a second referendum is likely to fail if a sizeable chunk of Labour MPs vote against it. Just eight Conservative MPs have backed calls for a public vote (nine if you include Anna Soubry who has since quit the party). That’s not enough to counteract the expected number of Labour rebels. Fourteen Labour MPs voted against Cooper’s amendment to delay Brexit on 29 January, and a further 12 abstained.