Intense discussions are taking place at Westminster that could lead to the emergence of a new centrist party consisting of six or more disaffected anti-Brexit Labour MPs along with the involvement of some Conservatives and the backing of the Liberal Democrats.

Labour MPs reported that some of those involved had lobbied backbench colleagues they thought were sympathetic as to how they could “make the shift” away from a tribal loyalty to the party.

The argument put forward was that the set of values that had drawn them to the Labour party, such as European solidarity, free movement, liberalism and anti-racism, could now be found elsewhere.

Those involved in the talks say frustrations over pro-Brexit policies pursued by Jeremy Corbyn and Theresa May, coupled with Labour-specific concerns about antisemitism, have taken a handful of MPs to the point where they are seriously considering quitting.

Labour MPs at the centre of the discussions include Chris Leslie, Chuka Umunna, Angela Smith and Gavin Shuker, signalling their intention to ratchet up the pressure on Corbyn in the hope he will whip his MPs to back an amendment calling for a second referendum.

“It’s time to start to make them realise that this is existential for the leadership,” said one potential splitter.

Luciana Berger has also been seriously considering her position as a Labour MP because of her dissatisfaction at the party’s approach to Brexit and the handling of antisemitism cases.

Close friends within Labour have been trying to persuade Berger, the MP for Liverpool Wavertree, to stay over recent days. Some party colleagues say that if she were to go it could represent a tipping point.

Conservative MPs considering their futures, according to those involved in the talks, include Sarah Wollaston, the MP for Totnes, Anna Soubry, the MP for Broxtowe, and Heidi Allen, who represents South Cambridgeshire.

The three have cooperated closely with Labour MPs as part of the People’s Vote second referendum campaign, and were all lead signatories of an amendment on Thursday that forced the government to agree to release no-deal cabinet documents.

Those involved in the discussions believe that a crunch point could come at the end of February, when pro-EU Labour MPs desperately want Corbyn to back a second referendum and restless Conservatives want May to rule out no deal if she cannot get a revised Brexit agreement through parliament.

A source in the People’s Vote campaign said: “Whatever happens, it is important to emphasise this is nothing to do with our campaign which is strictly and proudly non-partisan, involving supporters from all parties and none.”

Another idea circulating is that the new group could be called the Reformist party, with the Lib Dems contributing national and local resources. “There are a lot of generals here without an army – well the Lib Dems have an army of members,” one MP involved said.

A Labour MP contacted by members of the group said he believed there were around a dozen MPs in his party close to quitting. Those involved in the organisation are understood to have conducted significant polling, including in target constituencies.

“I honestly believe this is imminent. You will see the values emphasised first, rather than policies to help people make that change. There are the names that are public but others are involved, including in the organisation of it, who have never been named,” the MP said.

Labour strategists say they are relaxed about a potential breakaway, arguing that the figures involved are unlikely to be of the political standing of the four former cabinet members who helped found the Social Democratic party in 1981.

They also believe there is a firm majority in the shadow cabinet against a “people’s vote” and continue to hope May will ultimately be forced to soften her red lines and shift towards something more like the form of Brexit they have proposed.

The Momentum founder, Jon Lansman, issued a stark warning to MPs considering leaving the party that their project would be rejected by voters. “Chris Leslie, Chuka Umunna and Gavin Shuker are marginal figures with marginal politics,” he said.

“This is very different to the SDP breakaway in 1981. I was there, and I remember at least a certain level of public support for their policies. The situation is completely different now. Socialism has gone mainstream, a Blairite programme has no support amongst the public and parties pursuing similar programmes across Europe have seen their vote share plummet.”

Some in Labour appear to be goading the grouping to split. On Thursday, Momentum released a spoof Valentine’s Day video aimed at Umunna, set to the song Please Don’t Go. It urged him to stay in the party, but concluded: “If you go we’re keeping the house xxx.”

Local Lib Dem parties in some constituencies, such as Wavertree and Totnes where it has a presence, have been told to be receptive if any MP were to quit Labour or the Conservatives, even if they do so to sit in Westminster as an independent.

Party insiders say the Lib Dem leader, Vince Cable, could step down after the local elections in May, creating a vacancy for a leader of any new movement. They, too, have been studying the history of the SDP and say the Lib Dems could be open to anything from a full merger to an alliance or supporting independent candidates.