Two-thirds of EU citizens would back Britain rejoining the bloc, while most UK voters say Brexit has been bad for the issues they care about and want closer ties, including levels of integration – such as free movement – long seen as toxic, a survey has found.

Ten years after the Brexit referendum, the polling by the European Council on Foreign Relations (ECFR), a thinktank, found 66% of respondents across 15 countries felt UK membership was a very good, good or “neither a good nor a bad” idea.

The average comfortably exceeded those favouring a closer relationship (59%) or the status quo (46%). Support for rejoin ranged from lows of 56% in Bulgaria and 59% in France and Italy to highs of 75% in the Netherlands and Denmark.

Even voters for far-right and EU-critical parties said they would support closer relations between the bloc and the UK, including a majority of backers of Poland’s Confederation (71%), Germany’s AfD (58%) and France’s National Rally (58%).

Many European leaders have reflected this view. France’s president, Emmanuel Macron, has said the door is “always open” and Spain’s prime minister, Pedro Sánchez, has said Spain would “absolutely” support British membership.

Alexander Stubb, Finland’s president, has explicitly named the UK as a candidate for membership, saying: “We need a UK voice in Europe. We really miss you guys.” In May, the European Green party formally invited the UK to rejoin.

In the UK, the polling, carried out in May, found voters across party lines, including supporters of Reform UK, believed Brexit had had a negative impact on the country and on many key issues at the heart of the debate a decade ago.

British respondents said leaving had hit their main priorities: the cost of living (66%), the economy (65%), youth opportunity (57%), illegal immigration (56%) and trade (56%). Even most leave voters (58%) said Brexit had made illegal immigration worse.

Asked to identify the primary benefits of Brexit, the most common response, by a wide margin, was “don’t know”, followed closely by “none of the above” – suggesting most British voters now feel Brexit did real damage for no apparent upside.

That overwhelmingly negative verdict on the decision to leave translates into a strong desire for a closer relationship with the bloc: 75% of UK respondents were in favour. Asked about trade and economic ties, 66% said they should be very or slightly closer.

Perhaps most strikingly, a large majority (63%) of respondents – including 57% of those who voted leave in 2016 – said they would now accept freedom of movement in exchange for closer trading ties, with only 18% rejecting it.

Even among voters who said their top concern was immigration, 44% said they would back freedom of movement as part of a closer economic relationship, suggesting one of the core drivers of the Brexit vote is no longer central to the UK debate.

The report’s author, Mark Leonard, the director of the ECFR, said the polling showed the EU was open to the UK’s return and that the British public had fundamentally moved on from 2016 – meaning Europe was now a political opportunity for the UK government.

“Brexit was the insurgent vehicle for a nation rejecting the status quo,” he said. “A decade on, Brits realise their hopes for a better life outside the EU are unfulfilled and Brexit is undermining the UK’s ability to manage the issues they care about most.”

Leonard added that the data showed the “vast majority of citizens are open to a closer relationship”, revealing the existence of a “very broad permissive consensus for going far beyond the government’s current reset”.

The report identified three main voter camps in the UK: “optimists” (28%) who view European alignment as a geopolitical necessity; “realists” (35%) who support closer ties but still value US ties; and “loners” (27%) who still prioritise national sovereignty.

Overall, the survey found British voters favoured Europe over the US as a preferred security partner, with just 18% now viewing the US as an ally and 58% favouring closer defensive relations with Europe, compared with 19% for the US.

A majority of British voters do not want to buy more weapons from the US, while more than 60% would prefer to follow a “buy European” policy. Almost two-thirds (63%) also want the UK to participate in developing an alternative European nuclear deterrent.