An economist who has advised John McDonnell and transport union boss Manuel Cortes are among those who have signed up to Labour for a “people’s vote”.
General secretary of the TSSA Mr Cortes said recent concerns over Brexit raised by Airbus, Siemens and the CBI were “a wake-up call for our movement to fight it tooth and nail”.
He added: “The only Brexit on offer by the Tories is a kamikaze one.
“It will destroy jobs, our manufacturing industry and workers’ rights.
“Make no mistake – high-priest Brexiteers, from Nigel Farage to Iain Duncan Smith, want to finish off the job Thatcher started.
“Their hatred of our class is renowned and we must fight them, giving them no quarter.
“There is nothing in Brexit for working people.
“That’s why we are now seeing an increasing number of trade unions coming out against it.”
The group also includes members of the left-wing Momentum organisation that supports the Labour leader.
It wants the Labour Party to put clear distance between it and the Conservatives by supporting a “people’s vote” on the final Brexit deal.
It will then campaign for “a public vote on the deal, with an option to stay in the EU should voters reject it”.
The group says that its first priority is the election of a “radical Labour Government”.
Ann Pettifor, who was appointed by Mr Corbyn in 2015 to a panel of experts advising Labour on economic policy, is also a supporter of the group.
So too is Momentum member Michael Chessum, who worked on Mr Corbyn’s second leadership campaign.
Mr Chessum said: “We have no interest in undermining the current leadership – quite the opposite.
“Tory Brexit would be a disaster for the prospects of a radical Labour Government – it would deregulate and shrink the economy and attack working class people and migrants.
“We cannot ignore that any longer and many people who are not die-hard Remainers will be reaching the same conclusion.”
The group also describes the Norway-style EEA deal after Brexit as “untenable” and argues that “the effects of Brexit would make the prospects for a socialist Labour government much worse”.
It comes after tens of thousands of people from across the political spectrum marched in London on Saturday calling for a “people’s vote” on the final Brexit deal.
They included Liberal Democrat leader Sir Vince Cable, ex-Labour NEC member and actor Tony Robinson and Green party co-leader Caroline Lucas, but no current senior Labour figures.
The crowd at Saturday’s march could be heard chanting “Where’s Jeremy Corbyn?”, but the Labour leader was in Jordan visiting refugee camps.
Shadow chancellor John McDonnell was in London but did not attend.
He told a conference of the Open Labour grassroots group he would prefer a general election to a second referendum if a Brexit deal cannot be agreed and approved before the UK leaves the EU.