A majority of all Britishers would vote to leave the European Union if a referendum was held now, while two-thirds of all French people believe the 27-nation EU was headed in the wrong direction, a survey showed.
The Gallup Europe poll also showed that a rising anti-EU sentiment and speculation over the UK's exit could pave the way for nationalist candidates in the 2014 European Parliament elections.
Both the French and the British were losing faith in their national leaders.
62% of all French respondents thought the EU was moving in the wrong direction, while 86% disapproved of President Francois Hollande's leadership. In the UK, 56% of all respondents said the EU was moving in the wrong direction, while 82% disapproved of Prime Minister David Cameron's policies, the survey showed.
The long-drawn-out economic crises was also diverging opinions in Germany and France, the top two eurozone economies. "The French-German axis that provided the largest basis for common European policy in the past is now weakening, reflecting the diverging mood in the two countries," Gallup's Anna Manchin wrote in an analysis.
"The French are losing confidence in globalization and growing insecure in their position within Europe. Our findings reflect this turn in France away from the EU toward more pressing national problems."
France fell into recession in the first quarter of 2013 after economic activity shrunk 0.2%, a third contraction in the last four quarters, and unemployment has risen for 24 months in a row.
A good number of people in France (45%) approved of Germany's leadership in the EU. The results showed that 35% in the UK and 54% in Germany approved of Deutschland's ability to lead.
750 people across six countries -- Britain, Denmark, France, Germany, the Netherlands and Poland -- were polled in May. Most approved of Chancellor Angela Merkel's handling of the eurozone crisis.
An earlier survey by US-based Pew Research Centre, in May, sounded an alert to how support for the European Union had dropped to 45% from 60% a year ago.