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, research mapping voter attitudes 10 years after the Brexit referendum shows.

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

While three in five (61%) of all voters support 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% on Greens, the polling found.

Four in 10 Conservative supporters and one in five Reform voters also backed the policy, Best for Britain found.

“We think that there is inherent risk with halfway houses,” said Tom Brufatto director of policy and research at Best for Britain which maps the space for public policy on EU relations.

They tested six scenarios including continuing with Labour’s current low-ambition policy, keeping Boris Johnson’s deal, diverging further, joining the customs union and single market, and the full-fat option of 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 of 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 current policy is to align with but not join the single market which means it has no say in the shaping of regulations and directives.

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

Divergence on rules since Brexit in 2020 has seen the UK diverge on 76 rules and regulations in relation to the current negotiations over a sanitary and phyto-sanitary (SPS) agreement 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 said was Labour’s “strategy of silence” around Brexit and political calculations may have to shift as the loss of the liberal voter base on issues such as Brexit could be more damaging than loss to pro-Brexit parties.

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

Neil Kinnock, the former Labour leader, said Brexit had inflicted enormous damage on the UK and he believed the Labour party 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 [rejoining].”

Anand Menon, director of UK in a Changing Europe, which has tracked Brexit for almost 10 years, said Labour’s own 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 now 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 a ever-bigger rule-taker with all the political attention and administrative work that needed in Westminster.

Aligning with EU regulation would mean a unending cycle of regulation and watching over political soldiers to see that all regulations were transposed so “divergence doesn’t happen accidentally”.

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