45% of Europeans say they believe the vaccine roll out has been handled badly.
Just two in ten older Europeans think the EU has handled the COVID-19 vaccine programme well, according to the latest 'eupinions' poll.
The report, Europe Today and Tomorrow: What Europeans Want, provides 'mixed reading' for the EU.
It was conducted for the Europe's Stories project of the Dahrendorf Programme, based at St Antony's College in Oxford.
In total, only 25% of those surveyed say they believe the vaccine roll out has been handled well.
Concerns about the programme increase in line with age and more than half of those aged 50-69 say it has been fairly or very badly handled.
The report states, 'There is clear dissatisfaction with the EU's distribution of COVID-19 vaccines and many respondents agree that freedom of movement has brought more costs than benefits for their country.'
Some 44% of those surveyed report not having personally benefited from freedom of movement, 37% say it has brought more costs than benefits for their country.
But there were wide national differences, with almost half of French respondents thinking that freedom of movement has had more costs than benefits, this compared with 40% in Germany and just 28% of respondents from Poland.
The report comments, 'Perhaps not a surprising finding, given so many Poles have benefitted from free movement.'
Seven in ten surveyed say they identify as Europeans (as well as having other identities). But, here again, national differences are revealed, with some 86% of Polish and 84% of Spanish agreeing with this, compared with 60% of French and 63% of Italians.
Participants were also asked if taxpayers in richer states should contribute more to the EU budget - 'to ensure a minimum standards of living across all member states'. Some 66% of Spanish support such measures, while 40% of Germans back more taxes.
However, more than 60% thought the EU should take more decisions about employment and social protection because of the threat posed by automation to jobs.
Although there was significant support for greater integration, with 28% backing this, just 13% support a single European government. This was only slightly ahead of the percentage who said the EU should no longer exist.
But more over 50s thought the Union should no longer exist, than thought there should be a single government. As with many questions, French respondents were more hardline - with 15% saying they would like the EU no longer to exist.
Meanwhile, the top priority for new border guards, according to those survey, should be to, 'Prevent unlawful entry to the EU.'
The second priority should be to fight cross border crime and terrorism and just 12% of older respondents thought new border guards should ensure the safety of those attempting to enter the EU.