Almost half of Britons would vote for the UK to leave the European Union in a referendum, according to a newly-published poll.
Some 49% said they would back British withdrawal, while 28% indicated they would vote to stay in the EU, the YouGov survey found.
Another 17% said they did not know how they would vote if there was a referendum.
The poll, conducted amid British calls for the EU budget to be frozen or cut in real terms, also found that only 29% felt the UK to be influential in Europe.
By contrast, 59% of Germans believed their country to be influential in the EU.
The majority of Germans also supported Germany remaining in the Union, by 57% to 25% against.
YouGov said the findings demonstrated the difficulties facing Prime Minister David Cameron and German chancellor Angela Merkel, who met in Downing Street last night, to reach an agreement on the EU budget.
Mr Cameron is calling for a real-terms freeze - despite the Commons voting last week for a cut - while Mrs Merkel is more preoccupied with sorting out the eurozone crisis and will allow a small rise in the budget.
The Prime Minister has indicated he does not have "high hopes" of reaching a deal with all 27 EU members, raising the prospect that he will wield the veto again.
YouGov's director of political and social research Joe Twyman said: "The noticeable distance between how people in Britain and Germany feel about their country's membership of the European Union underlines the scale of the challenge facing both David Cameron and Angela Merkel in trying to come to an agreement over the EU's budget.
"On one hand, Merkel must try and bring member nations onside with her pro-European, inclusive agenda - which includes an increase in the budget.
"In contrast, Cameron must attempt to be perceived as a constructive member of the Union, while at the same time trying to satisfy public opinion in his own country, where a significant proportion are opposed to Britain's membership in the EU."
YouGov interviewed 1,637 British adults and 1,018 German adults between October 19 and 28.