People in the EU's leading member states remain loyal to the organisation's founding values of openness and liberalism, the Guardian's five-country poll shows. Despite the economic crisis and the rise of extreme political parties, an overwhelming majority of Europeans describe themselves as liberal – even on issues such as gay rights.

More also continue to support the right of people to migrate within the EU in search of work than oppose it. While the results reveal high levels of opposition to EU migration, – notably in Britain – a small overall majority of those polled in France, Germany, Spain, Poland and Britain approve. But attitudes in all countries questioned are less tolerant when it comes to migration from outside the EU. A quarter of Europeans list non-EU migration as the leading or second threat to Europe's future.

The poll calls into question Britain's long-standing claim to openness and tolerance: opponents of EU migration in Britain outnumber supporters by two percentage points. In Germany, by contrast,the support for migration outscores opposition by 30 points, with 49% of Germans in favour of the right to move states. In France the net lead is 41 points, with 55% in favour and in Spain the lead is 57 points, with 67% in favour.

Guardian Europe poll: click image or graphic and data

However, a narrow plurality are against migration from outside the EU. Across the countries polled opposition stands at 37% against support at 32%. Again, Britain is notably hostile to non-EU migration: 47% say they are against it, while only 20% are in favour – with 23% of Britons saying they are "strongly hostile".

By contrast 46% of Poles are in favour against 25% who are against. Poland is the only state among those surveyed where approval leads opposition. In Germany, 30% approve while 37% do not. In France, the figures are 30% to 39% and in Spain 33% to 39%.

Overall, 62% of the more than 5,000 people polled across Britain, Germany, Poland, Spain and France say they see themselves as "liberal" rather than "traditional" on social issues. While 24% of Europeans claim to be "very liberal", only 4% think they are "very traditional", in answer to a question specifically asking their approach to issues such as marriage, women's rights and gay rights.

Notably even Poland and Spain, both strongly Catholic nations and relatively recent EU entrants, emerge as much more liberal than traditional. Almost three-quarters of Spaniards polled choose to describe themselves as either very or fairly liberal; narrowly ahead of Germany, then Britain, France and Poland. It is possible that the internet-savvy group of working age people surveyed in the poll – carried out online – are more likely by definitionto see themselves as liberal.

Pensioners, not surveyed, may be more traditional. But the samples were weighted to be representative of the demographics of each country.

The heavy balance in favour of liberal values in the poll also suggests this is indeed how modern Europeans see themselves.

In Spain, for instance, 30% say they are "very liberal" and a further 42% "fairly liberal" against only 6% who say they are "fairly traditional" and 2% "very traditional". That pattern is repeated elsewhere. In Germany, 68% say they are liberal against 9% traditional. In France, 59% against 14%. In Britain, 60% to 19%.

Attitudes are different in Poland, where 31% of people see themselves as traditional against 49% liberal. Perhaps surprisingly, there is no sign that younger people, who grew up after the fall of communism, are any more or less liberal than their parents.