A cross-party group of MPs has formally launched a campaign to win support in the Commons for Brexit via a managed deal, arguing both a no-deal departure or a second referendum would cement political divisions and cause endless uncertainty.

The organisers claim up to 50 MPs so far may back the plan, which would involve using elements of Theresa May’s Brexit proposals as the basis for an agreement which Boris Johnson could steer through parliament, possibly in time for a 31 October departure.

Stephen Kinnock, the Labour MP whose amendment, using May’s plan as a possible focus for any extension, to a rebel bill seeking to prevent the UK crashing out of the EU was unexpectedly passed last week, said the group was “not about reproducing a carbon copy” of May’s three times-rejected plan.

Instead, he said, it would be modelled on the results of failed cross-party talks between May’s government and Labour, but with a consensual focus, aiming to bring a deal Johnson could negotiate with the EU and then get through the Commons.

“The fact is we are rooted in reality here,” Kinnock told a launch event at parliament. “This is not a unicorn. We have something here that is the basic foundations of a perfectly pragmatic deal that we believe can command a majority in parliament and also begin to reunite our deeply divided country. And even at this 11th hour we believe there is time to do it.”

This did not mean the MPs would support any deal, he added. “I don’t think this is about carte blanche.”

Caroline Flint, one of the leading Labour backbenchers wary of the party’s move towards backing a second referendum, said the group could countenance a Brexit delay until 31 January, but only if this was focused on securing a deal.

The aim of the group was, she said, to “show there is a sizable voice building across the house to secure a deal”. She added: “We may not be as loud as some voices, but we are a voice of reason here, trying to work through this process holding all sides to account.”

Labour MP Caroline Flint says the aim is to ‘show there is a sizeable voice building across the house to secure a deal’. Photograph: Suzanne Plunkett/Reuters

Several of the dozen or so MPs at the launch event urged the necessity of compromise. Rory Stewart, the former international development secretary who was among 21 Conservative MPs ejected from the party after supporting backbencher moves to block a no deal, said the wrong sort of Brexit could cause divisions for decades.

“If we were to go for a no-deal Brexit, we would have about half the country very angry and alienated. They would feel about no-deal Brexit the way that many of the people I’ve seen recently in the north-east feel about Mrs Thatcher,” he said.

“On the other side, if we want for a full remain through a second referendum, you would have about half the country feeling incredibly alienated, angry and tricked.”

The broad aim of the group is to both maintain pressure for a managed Brexit and to raise sufficient support among MPs such that if a deal was tabled, enough Labour MPs could potentially vote for it to give the government a majority, bearing in mind a number of hard-Brexiter Tories could oppose it.

Norman Lamb, the sole Liberal Democrat MP involved, said he was hopeful that with Johnson now mandated under law to seek an extension to Brexit if he cannot find a deal, this could be an escape route for the PM.

Lamb said: “He’s completely got himself boxed in. He has to find a way out of this mess, and this is the way out of the mess.”