In a survey of more than 6,000 people – across Belgium, France, Germany, Hungary, Italy, Poland, Spain and Sweden – 45 per cent said they wanted their own vote of whether to remain part of the 28-country bloc.
And in news likely to shock Brussels officials, almost half of Italians (48 per cent) and four in ten Frenchmen and Swedes (41 per cent and 39 per cent respectively) said they would vote to leave the EU if they were given the chance.
By contrast, just one in five (22 per cent) Poles would vote for their country to leave the EU if an in/out referendum was held.
The results of the Ipsos-MORI poll come as a major snub to EU bosses on Europe Day, with today supposed to be a celebration of EU integration and unity.
EU staff are given today off as part of the annual celebration, with many EU buildings open to the public.
But the Ipsos-MORI survey of nine big EU countries – including Britain and representing around three-quarters of the EU population and approximately 80 per cent of its GDP – suggests growing euroscepticism across the continent.
With Britons due to decide on their own EU membership on June 23, the poll suggested EU bosses are right to fear a ‘domino effect’ in the event of a Brexit vote.
Nearly half (48 per cent) of those asked in EU countries believed if Britain quit the EU next month then other countries would follow.
One in ten (11 per cent) believed the EU would even be disbanded altogether by 2020.
The survey also revealed Europeans believe Brexit will be more harmful to the EU than to the UK itself.
Half of Europeans think Brexit would have would have a negative impact on the EU’s economy and for the EU’s influence on the world stage (51 per cent and 48 per cent respectively).
But less than two in five think Brexit would be negative for Britain’s economy or position on the world stage (36 per cent and 38 per cent respectively).
People in India, Italy, Poland, South Africa and the US even think leaving the EU would have a net positive impact on Britain’s economy, although only those asked in India and the US believe it would boost Britain’s standing in the world.
Surprisingly, Britons were more pessimistic over the chances of Brexit than other EU citizens.
Only 35 per cent of Britons asked believed the UK would actually cut its ties with Brussels this summer, compared to 60 per cent of Italians and 58 per cent of Frenchmen.
Opinion on the long-term character of the EU was split, with a quarter of Europeans (23 per cent) believing their country should