The map reveals the majority of citizens in the three southern member states of Italy, Greece and Cyprus do not believe they have benefited from being part of the union.
And in Austria, Bulgaria, the Czech Republic and even France, those who feel positively about the EU fall below 60 per cent.
The map is based on the Parameter survey, a series of interviews with those living in all the EU’s member states.
It indicates that Brussels chiefs have a battle on their hands to convince a large number of countries not to follow Britain’s example and push to breakaway.
In total, 27,881 EU nationals were asked the question: “Taking everything into account, would you say that your country has on balance benefited from or not from being a member of the EU?”
Italians had the poorest view of the bloc, with just 39 per cent saying the country had benefited from membership.
And that could send alarm bells ringing with parliamentary elections in the country looming and the prospect of Eurosceptic politicians tipping the balance of Italian politics against the EU.
Cyprus was also highly sceptical, polling just 45 per cent, with Greece on 48 per cent.
The poll, which took place between September 23 and October 2 this year, saw Europhiles in the UK only muster 55 per cent.
Ireland had the most positive response, with 90 per cent seeing benefits to membership.
Malta, Lithuania, Luxembourg, Poland, Denmark and Estonia all saw scores of at least 80 per cent.
Despite the mixed picture, European Parliament president Antonio Tajani said the results were “positive and encouraging”.
And he seized on the figures to push for further influence.
He said: “The result of the survey is very positive and encouraging. It shows that the confidence in our institutions and our work continues to grow and that we are leaving the crisis of recent years behind.
“Naturally, in some areas, views vary from member state to member state. This should inspire us to step up our efforts to tackle the concerns expressed.
“In general, people increasingly see the EU as a key player in tackling the big challenges and protecting them against common threats such as terrorism, unemployment or poverty and exclusion.”
He went on: “I also take the results of the survey as a mandate for the European Parliament to increase its key role in shaping the EU’s future.”