A grassroots group of Jeremy Corbyn supporters and trade unions is to launch a major UK speaking tour, billed as the leftwing campaign to remain in the EU.

The Left Against Brexit tour will attempt to persuade Corbyn and his allies of the leftwing case for a pro-EU position and will argue that the party can reap electoral benefits from a shift.

Speakers on the summer tour of British cities will include Manuel Cortes, the general secretary of the transport union TSSA, Michael Chessum, who was on Momentum’s first steering committee, the Labour MEP Julie Ward, the former shadow minister Catherine West, and the Green party co-leader Caroline Lucas.

Organisers will argue that a Corbyn-led programme of economic reform would be hampered by a damaging departure from the EU, threatening jobs and investment.

The speakers will not call for a rerun of the referendum on EU membership, but for Corbyn to formally reject leaving the EU and make the case that a vote for Labour would be a vote to remain – although the UK is set to formally exit the bloc before the next scheduled election in 2022.

“There is nothing about Brexit that will make life better for the working class,” Cortes said. “It was a rightwing brainchild won – and only narrowly – on a deceitful programme of dog-whistle racism and the big lie that the NHS would get £350m a week.

“The left should unite now and come together to stop this Tory act of war against our class. Our job is always to defend our people against the boss class. Supporting Tory/Ukip Brexit is unacceptable class collaboration. Full stop.”

Cortes said the time was right for Labour to reconsider its message on Brexit. He called for the party to “come clean with the electorate [to] say the Brexit squeeze ain’t worth the juice”.

“The Corbyn promise of new economic settlement at home is now our priority,” Cortes said. “Frankly, there is no one better placed than Jeremy to call for peace and reconciliation with Europe. Pulling out of Brexit, not Europe, is now the bold offer we need to make if we are to win an election and begin to properly rebuild prosperity at home.”

Ward, the Labour MEP for north-west England, said the fight to remain in the EU would “embody the spirit of previous generations who stood shoulder to shoulder against the fascists in Germany, France, Spain and elsewhere”.

She said Britain would be “toothless” outside the EU against a growing tide of racism and xenophobia. “A Corbyn-led Labour government could lead the charge to reform the EU from within, giving hope to millions of young people across Europe,” Ward said.

“This Left Against Brexit tour opens the way for the majority view in the Labour party to shift the party back to where it belongs – at the heart of the EU, arguing for a more fair and just world for the many.”

Lucas, who will step down as Green party co-leader in the autumn, said an “independent, left voice against Brexit” was needed in the debate. “We’re going to make the radical case for staying and leading in the EU.”

Momentum, the grassroots pro-Corbyn group, is not part of the tour and sources said the group backed the Labour leadership’s current position to pursue an EU exit that protects jobs.