In a joint letter, the SNP, Liberal Democrat, Green Party and Plaid Cymru leaders called on Mr Corbyn to join forces with them “in opposing the Tories’ damaging plans”.
The Labour leader has previously refused to engage with other parties that are campaigning against the Government’s plans for a hard Brexit.
The latest attempt to encourage Mr Corbyn to cooperate comes as he faces mounting pressure from within his own party to soften his stance on Brexit and commit to keeping the UK in the single market and customs union.
Carwyn Jones, the Welsh First Minister, told The Independent he expected Mr Corbyn to announce a shift in policy in favour of staying in the customs union “within months” and warned that leaving the bloc would be “economically daft”.
Earlier in the week some Labour MPs said their leader needed to “get off the fence” and stop “hedging bets” on Brexit.
Mr Corbyn has so far suggested the UK should leave the single market and existing customs union. He has proposed forming a new customs agreement after Brexit and wants the UK to have unfettered access to the single market.
Last month the Labour leader was empty-chaired at a cross-party summit designed to help boost coordination between the political parties opposing the Conservatives’ stance.
In their letter, the SNP’s Ian Blackford, Lib Dem leader Sir Vince Cable, Plaid Cymru’s Liz Saville Roberts and Green Party co-leader Caroline Lucas again urged Mr Corbyn to meet with them to discuss Brexit.
In their letter, the four leaders wrote: “We write to you today, ahead of your planned discussions on Labour’s Brexit policy, to urge you to rethink your opposition to the UK’s continued membership of the single market and customs union.
“With each passing week we see mounting evidence of the perils of a hard Brexit and the leaked papers last week make it clear that leaving the EU will, in all circumstances, harm the economy of every nation and region in the UK.
“We believe that the big decisions facing us, over membership of the single market and the customs union, can no longer be ducked.”
Arguing that a hard Brexit “makes progressive goals far harder to achieve”, they said the “best protection for our economy and in turn our public services, and to protect jobs, is to remain in the single market and customs union”.
The leaders added: “Though all party leaders must take account of multiple factors when making decisions of this magnitude, we urge you to focus specifically on the effects that a hard Brexit will have on people who are already suffering in this country.
“By campaigning for the UK to remain permanent members of the customs union and single market you could change the course of Brexit, and in turn protect our economy and society from some of its worst effects.
“Please do consider changing your position, and joining us in opposing the Tories damaging plans.”
The group has also invited Frances O’Grady, general secretary of the Trades Union Congress, to attend a second meeting of the cross-party alliance.
Mr Blackford said: “It is vital that all opposition parties in Westminster work together and put the brakes on a hard Brexit. We will work to protect our membership of the Single Market and Customs Union – which puts jobs and living standards front and centre of the Brexit negotiations.
“There is still a seat at the table for Jeremy Corbyn to join with other Westminster opposition leaders and work with us before it’s too late.”
Liberal Democrat leader Sir Vince Cable added: “It is time for Labour’s leadership to join us and fight for Britain’s economic future, rather than allow the Conservatives to steer the UK towards a damaging and unmandated hard Brexit.
“This means, at the very least, they work alongside us to keep the UK within the single market and the customs union, a position the overwhelming majority of Labour’s members and parliamentarians support.”
Ms Lucas called on Labour to “ditch their fence sitting and join us in campaigning for Britain to remain a member of the single market and customs union”, while Ms Roberts said there was “a rare opportunity to force the Tories into taking the sensible option – but only if the Labour Party work with us”.
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