Almost half (45 percent) of all respondents think that their own country should have its own referendum, and in Italy (58 percent) and France (55 percent), majorities wanted referendums, the pollster Ipsos MORI reported on Monday.
The online survey of between 500 and 1,000 online adults aged under 65 in Belgium, France, Germany, Hungary, Italy, Poland, Spain and Sweden found marked differences between the countries in attitudes towards EU membership.
In total, around one third of respondents said they would vote to leave the EU in a referendum on membership, a proportion which was higher in Western Europe.
Almost half of Italians and roughly four in ten people in France (41 percent) and Sweden (39 percent) say they would vote to leave the EU.
For comparison's sake, just 22 percent of Poles said they would vote for their country to leave the EU if a referendum was organized now.
The survey for ITV television found that support for staying in the EU is at 42 percent, and support for leaving is 40 percent. Six percent were undecided, and 13 percent said they did not know how they will vote on June 23, the newspaper Metro reported.