Jeremy Corbyn has told Labour MPs to hold firm to the party’s position on Brexit, calling it a “false choice” that they had to vote for Theresa May’s final agreement or risk a no-deal outcome.

Corbyn and the shadow Brexit secretary, Keir Starmer, addressed the private meeting of Labour MPs and peers on Monday night, amid speculation that up to 30 MPs would consider voting for any final Brexit deal brokered by May because of concerns about the backlash from leave-supporting constituencies and the risks of a failure to reach a deal with the EU.

Several MPs including John Mann and Caroline Flint expressed concern about the prospect of Labour voting down a deal, but Corbyn and Starmer said it would not be a “straight choice”, sources said.

Earlier on Monday, the Labour MP Gareth Snell, whose Stoke-on-Trent Central constituency voted 69% for Brexit, tweeted “no self-respecting Labour MP” would be willing to walk into the same voting lobbies as hard Brexiter Tories hoping to force a no deal.

Gareth Snell MP (@gareth_snell) I’m sure no self-respecting Labour MP will walk into the same lobby as Andrea Jenkyns and the hard-right ERG when the options are known. https://t.co/q66eDMAkKV

A Labour source said Corbyn told the room that splits in the Tory party meant no deal on offer could command support from the whole house. The source suggested that Corbyn had hinted to MPs he believed Labour may be able to force a softer Brexit position, one that could meet Starmer’s “six tests”.

“If she is unable to bring anything back, or brings back the kind of package currently on offer, that won’t be able to command support in the House of Commons,” the source said. “In those circumstances, Labour can put forward [its offer] which could command a majority in parliament and does command majority support in the country. We need to find a way towards that outcome.”

Starmer and Corbyn stressed Labour had its “own plan” for Brexit, the source said. “Part of the concern, which the government wants to talk up, is that there is only a no deal alternative. That is clearly not the case and it is clearly not what the majority of MPs want.”

Earlier in the Commons, Corbyn had emphasised that Labour would not accept that a vote against May’s deal would be an endorsement of no deal. “The choice for this parliament should never be her deal or no deal: if this government cannot get a good deal for this country then it has to make way for those who can,” he said.

Corbyn said the UK and EU should negotiate a “permanent customs union” to protect jobs and manufacturing and said May should be able to offer the Commons a deal that could command Labour support.

“The prime minister faces a simple and inescapable choice: be buffeted this way and that way by the chaos of her own party, or back a deal that can win the support of parliament and the people of this country,” he said.