Support for rejoining the EU rather than simply rejoining the single market is growing among British voters, with more than 80% of Labour, Liberal Democrat and Green party supporters favouring this option, according to research mapping voter attitudes 10 years after the Brexit referendum.

Labour’s “muted” approach to the issue means it risks losing support among progressive voters and in “red wall” constituencies, experts have said as part of research by Best for Britain.

While 61% of all voters supported the government’s current approach to EU relations, only 19% did so “strongly”, the research showed.

A full return to the EU was supported by 53% of all voters with support at 83% among Labour voters, 84% Liberal Democrat and 82% Green, the polling found.

Of Conservative and Reform voters, 39% and 18% backed the policy respectively, Best for Britain found.

“We think that there is inherent risk with halfway houses,” said Tom Brufatto, the director of policy and research at Best for Britain, a civil society group that says its aim is to “fix the problems Britain faces after Brexit”.

Researchers tested six scenarios, including continuing with Labour’s low-ambition policy, keeping Boris Johnson’s deal, diverging further, joining the customs union and single market, and rejoining the EU.

Rejoining the customs union and single market, which Labour strongly opposes, would be a challenge politically as it would reopen the divisions of the past.

“It requires a deep conversation about sovereignty, because [rejoining the customs union and single market] requires outsourcing large parts of all of our regulation” and no party would “be able to carry the public with us as part of that protracted negotiation”, said Brufatto.

It would also mean the burden of rule-taking would increase daily. Labour’s policy is to align with, but not join, the single market, which means it has no say in the shaping of regulations and directives.

Labour’s attempt to reduce trading barriers for farm exports through a sanitary and phytosanitary (SPS) agreement provides a glimpse of the rule-taking to come.

Since Brexit in 2020, the UK has diverged on 76 rules and regulations in relation to the negotiations over the SPS agreement, which is designed to reduce paperwork for farm food exporters.

At an event unveiling the research in Westminster, the polling expert John Curtice criticised the effectiveness of what he described as Labour’s “strategy of silence” around Brexit. Political calculations may have to shift, he said, because the loss of the liberal voter base on issues such as Brexit could be more damaging than the loss to pro-Brexit parties.

Labour had lost about one in 10 voters to Reform but was losing one in four to the Lib Dems and Greens, he said.

Neil Kinnock, the former Labour leader, said Brexit had inflicted enormous damage on the UK and he believed Labour would one day campaign for rejoining, without putting a timeline on it.

“I’m 84 now and probably won’t see it, but the realisation [that it was best] and [in] the self-interest of the people, people will see it,” he said.

Anand Menon, the director of UK in a Changing Europe, which has tracked Brexit for almost 10 years, said Labour’s position betrayed inherent contradictions in its vision.

“Economically, I don’t think it’s sustainable for a government whose chancellor now goes around saying Brexit has cost the economy 8% of GDP, which is the highest side, to set against a reset that is worth just 1% growth.”

He said the Labour party was facing pressure from rivals to go further and faster but its current strategy to align on trade standards sector by sector meant the UK would become an ever-bigger rule-taker, with all the political attention and administrative work that needed in Westminster.

Aligning with EU regulation would mean constant monitoring to ensure “divergence doesn’t happen accidentally”.

“In a purely administrative sense, where we are now is very uncomfortable,” Menon said.