But the leftie leader is resisting the calls from 30 senior figures - saying the party should not give up powers which it will need in government to deploy state support for industry.
At the beginning of the party's annual conference, Labour lawmakers and trade union leaders wrote an open letter to their leader, calling on Jeremy Corbyn to "go further" than his current position to press for being part of the single market during any transition after Britain leaves in March 2019.
Seizing on the letter as evidence of a divide within Mr Corbyn's party, the Conservative MP Luke Hall said: "Labour are totally divided over Brexit".
Mr Corbyn's supporters secured an important victory in the party's ruling National Executive Committee (NEC) over changes to the leadership election rules.
In an interview with BBC1's Andrew Marr Show, the Labour leader repeatedly dodged the question of whether he would join picket lines on an illegal strike, but said he would "be with" workers demanding decent pay rises.
"What I said was that we need at least two terms of a Labour government to start to address issues of poverty and injustice and inequality in Britain and to build the houses we need in this country", said Mr Corbyn.
Instead, he said he believed a transitional period with full single market access should last for as long as is necessary and offered some support for continued migration.
The letter, which was also signed by the TSSA union's general secretary, Manuel Cortes, former Northern Ireland secretary Lord Hain and Liverpool mayor Joe Anderson, said Labour needed to present an alternative to the Tories' "destructive Brexit".
"The single market...has within it restrictions on state aid and state spending and pressures on it, through the European Union, to privatise rail and other services", he said. "I think we have to be quite careful about the powers we need as national governments".
He suggested that European Union rules could have prevented him as prime minister from intervening to prop up Britain's steel industry during its recent crisis, and would block a future Labour government from investing in industries.
"The idealistic, pro-EU, young people who have rallied behind Corbyn will be mortified to discover that he is working hand in glove with the Conservative Party to promote a "hard" Brexit".
Corbyn said a transitional period should last as long as necessary but it would not be as long as a decade.