A majority of Britons who voted to leave the EU would now accept a return to free movement in exchange for access to the single market, according to a cross-Europe study that also found a reciprocal desire in member states for closer links with the UK.

Russia’s invasion of Ukraine and Donald Trump’s election as US president had “fundamentally changed the context” of EU-UK relations, the report by the European Council on Foreign Relations (ECFR) thinktank said.

“There is a remarkable consensus on both sides of the Channel that the time is ripe for a reassessment of EU-UK relations,” it concluded, with closer relations being the most popular option in every country surveyed – and public opinion on the question well ahead of government stances.

Based on polling of more than 9,000 people across the UK and the EU’s five most populous countries – Germany, France, Italy, Spain and Poland – in the weeks after Trump’s election win in November, the ECFR study found the strongest enthusiasm for renewed ties were in Britain.

Perhaps the most striking finding was that 54% of Britons who voted leave, including 59% of voters in “red wall seats”, said in exchange for single market access they would now accept full free movement for EU and UK citizens to travel, live and work across borders.

This could be because the surge in net migration to the UK after 2016 meant that Brexit was no longer seen by its supporters as the answer on immigration, the report suggested.

Among all UK voters, 68% of respondents would now back free movement in exchange for single market access, with 19% opposed and majority support among supporters of every party apart from Reform UK (44% of whose voters also backed the idea).

A similar percentage of Britons supported a reciprocal youth mobility scheme for 18- to 30-year-olds, seen as a key ask for EU leaders in return for an improved Brexit deal but has so far been resisted by the British prime minister, Keir Starmer.

Given today’s global circumstances, the report said, the UK and EU should “go big and go fast” in restoring links. It added: “The EU and the UK are both very vulnerable to prevailing global events and a reset of relations is the single most effective way to make both sides stronger.”

The report argued that while EU politicians and officials have been sceptical about the idea of offering any special terms to the UK, and Starmer and his government are similarly cautious about pushing for improved ties, public opinion on both sides of the Channel appeared significantly different from those stances.

Among British voters, there was clear support for a closer relationship with the EU, with 55% saying they would back closer links with the bloc, against 10% preferring more distant ties and 22% wanting to keep them as they were now.

This belief was shared by many Conservative supporters, particularly over migration and security. It was mostly Reform UK voters who were more sceptical about the benefits of closer links to the EU.

Across the EU, pluralities in every country polled agreed: 45% of Germans said they wanted closer relations with the UK, as well as 44% of Poles, 41% of Spaniards, 40% of Italians and 34% of French.

“It is important to recognise that Brexit and the UK-EU future relationship matters more to UK respondents than to citizens of other states. But there is broad permission from European publics to recast relations,”the report said.

“There might be scepticism about special terms for the UK among EU officials and governments, but our poll suggests that public opinion is more pragmatic.”

Both UK and EU citizens, it continued, “are open to a much more ambitious and far-reaching reset than their governments have been envisaging”.

The report found about half of Britons believed greater engagement with the EU was the best way to bolster the UK economy (50%), strengthen security (53%), effectively manage migration (58%), tackle climate change (48%), allow Ukraine to stand up to Russia (48%), and for Britain to stand up to the US (46%) and China (49%).

There was similarly widespread backing among EU nationals for allowing some post-Brexit economic concessions in exchange for more cooperation on particularly important areas such as common security.

The polling found a majority of voters in Germany and Poland – and a plurality in France, Italy and Spain – thought the EU should be willing to make economic concessions to the UK in order to secure a closer security relationship. Majorities or near-majorities were also open to allowing the UK into the bloc’s research programmes.

This could extend to the idea of the UK “cherry picking” access to parts of the single market, with a majority of voters in Germany (54%) and Poland (53%) backing “special access”. Even in France, the least receptive to such ideas, 41% of respondents said they would back it, against 29% who would oppose it.

For EU citizens, the most important reasons for working more closely with the UK were to strengthen the bloc’s security (about 40% in Germany, Italy, Poland and Spain), and to stand up to the US and China.

Pluralities in all five EU countries said greater EU-UK cooperation was also the best way to increase the European economy (ranging from 38% in Spain to 26% in France), and manage migration efficiently (from 36% in France to 29% in Germany). Large numbers across the bloc felt Brexit had been bad for the EU.

While some Conservative and Reform politicians have suggested the UK should lean politically towards a Trump presidency at the expense of Europe, this did not seem to be a view shared by many voters. Asked whether the UK should prioritise relations with the US or with EU, 50% of Britons opted for Europe and only 17% for the US.

Europeans were similarly reluctant for their governments to follow Trump’s lead. “Donald Trump’s election and Putin’s full-scale invasion of Ukraine have hit British and European politics like a double hammer blow,” said the ECFR director, Mark Leonard, who authored the report.

“The Brexit-era divisions have faded and both European and British citizens realise that they need each other to get safer. Governments now need to catch up with public opinion and offer an ambitious reset.”