Jeremy Corbyn is under pressure from Labour grandees to embrace a softer Brexit plan, with party insiders threatening to trigger a rebellion over the issue at its autumn conference.

Senior Labour peers, including the former leader Neil Kinnock, former shadow justice secretary Charlie Falconer, and former chairman of the parliamentary Labour party Dave Watts, all told the Observer that they backed retaining Britain’s single market membership at least until a permanent deal could be hammered out.

Other senior figures are also looking at whether they can force an emergency vote at Labour’s conference, backing membership of the single market. Forcing such a vote would cause a major problem for Labour’s leadership, but represents a nuclear option and could be hard to engineer under party rules.

The tension within Labour comes as both main parties go into the summer with a series of unresolved internal issues over Britain’s future outside the EU. While the plan for a three-year transition deal set out by the chancellor, Philip Hammond, has gained support among the cabinet and Labour, major challenges remain in securing such an agreement. Meanwhile, ministers are still at odds over major parts of the final Brexit deal, from future immigration rules to the trade deals with countries around the world.

A crunch for Labour and the Tories is likely to come during an unpredictable and febrile party conference season in the autumn, with EU leaders due to decide in October whether to sanction the start of talks about Britain’s final Brexit trade deal. A sizeable group of Labour MPs and peers would like Labour to back keeping the UK in the European Economic Area (EEA) after Brexit, the so-called “Norway option”. Britain would have to accept unlimited numbers of migrants, obey new EU rules and pay a big annual fee.

Kinnock wants Britain to retain single market membership during any transition deal. “The only way to mitigate the dreadful instability that will be costly for communities and industry is to try to ensure that, at least for a transitional period, we retain participation in the single market or the customs union, or both,” he said.

“And what you are starting to hear now in the last couple of weeks is people in various areas – including business, manufacturing, finance, universities, science, research, as well as in politics – saying ‘we have got to consider a transitional arrangement that is fairly extended’, and secondly, calls for an ‘off-the-shelf’ arrangement like the EEA.”

He added: “I think that, as time and reality unfolds, the stated Labour ambition to protect jobs and investment and to participate in the single market will bring us to the position where we are trying to persuade the government to negotiate on that rational basis. So we will have to let time take its course in some ways.”

Falconer went further, backing single market and customs union membership for the transition and in effect for the permanent deal.

“I would strongly favour a transitional period in which we stayed inside both the single market and the customs union,” he said. “In that period you would need to adapt the European court of justice’s position, to represent the fact that the UK was outside the EU.

“We should ultimately seek to try to emulate as far as possible the single market arrangements [in the final deal]. On immigration, we need to be much tougher than we have been, but we have scope to toughen up within the existing rules. And we should be seeking to negotiate an emergency brake, on the basis that our arrangement is basically a single market and customs union basis.”

Facebook Twitter Pinterest Sadiq Khan, mayor of London. Photograph: Alicia Canter/The Guardian

Watts suggested he backed holding a second referendum once the Brexit deal on offer had emerged. “The British public were given a vote when they didn’t know what they were voting for,” he said. “Surely this is the time to give them a vote when they know what the detail is?”

He added: “There’s nothing more important than maintaining jobs and the economy, and I certainly would like to see the Labour leadership taking a stronger line when so much is at stake.”

Sadiq Khan, the London mayor, said this weekend that Brexit could be avoided should Labour use its next general election manifesto to back staying in the EU or endorse a second referendum on withdrawal.

In Brussels, there is a belief that the government is now “on the run” and that significant budget contributions could be on the cards for Britain until at least 2022. “It’s all very fragile, but the first sign of sanity breaking out is to recognise you are in a deep hole,” said a source.