If that happens, however, few fear specific consequences for their country.
This is the main finding of a new analysis from 'eupinions', an EU-wide, representative opinion poll commissioned by the German think tank, Bertelsmann Stiftung.
It comes just days before the In/Out referendum in the UK on 23 June.
It found that 54 per cent of EU citizens want the UK to remain in the EU. However, more than one in every five of those questioned (21 per cent) want the UK to leave.
Those who fear consequences for their own country are in the minority, with over two thirds of participants not expecting any repercussions for their homeland in the event of a Brexit.
The opinion poll took place in April with a sample size of 10,992 participants in the largest member states: Germany, France, Italy, Spain and Poland.
The survey found that opponents of a Brexit are clearly in the majority. While Spain and Poland are the countries most heavily in favour of the UK remaining (64 per cent and 61 per cent respectively), a slight majority of citizens in Italy (55 per cent) and Germany (54 per cent) are also opposed to the possibility of a Brexit.
Compared to the other largest EU states, it is the French who can most clearly envisage an EU without their British neighbours. 25 per cent of people in France are in favour of the UK's EU exit, while 41 per cent oppose it.
Germans and Poles are the most concerned, it found.
When it comes to the consequences of a Brexit for the EU and its member states, there is a lot of uncertainty among EU citizens.
Although they fear that the EU would be weakened, they do not foresee any negative consequences for their own countries. Some 45 per cent of EU citizens outside of the UK expect the position of the EU to be worsened by the UK leaving the EU.
However, an equal proportion of 45 per cent said that they did not believe anything would change for the EU. In terms of the changes that the participants could foresee, economic ones were at the forefront. 45 per cent believe that a Brexit would economically weaken the EU, while a third of those questioned - around 26 per cent - fear that the EU would suffer a loss of power without the UK.
In Poland (51 per cent) and in Germany (48 per cent), a narrow majority is worried about the consequences of a possible Brexit. Among the French, Spanish and Italians polled, however, the opinion prevails that a British exit would not have negative consequences.
However, a clearer picture emerges when participants are questioned about consequences for their own countries. Two thirds of EU citizens (67 per cent) outside the UK do not expect a Brexit to have an impact on their country.
This mood is also reflected in the larger member states, such as Germany (63 per cent), France (68 per cent), Italy (68 per cent), Poland (63 per cent) and Spain (71 per cent). Those who are relaxed and unconcerned about the prospect of changes for their country in the event of a Brexit are in the majority everywhere, with at least 60 per cent.
On Monday, Aart De Geus, Chair and CEO of the Bertelsmann Stiftung, told this website, "Even though many citizens are more preoccupied with their everyday concerns than they are with the results from London, all Europeans would lose out if the UK leaves."
Meanwhile, ALDE group leader Guy Verhofstadt said that Europe's reaction on a possible Brexit should be, "Out is out".
Speaking at the weekend on the VRT news show 'De Zevende Dag', Verhofstadt admitted that Europe does not work well in its present form, but argues that it would be stupid to pull out because of this.
According to Verhofstadt, the EU should be turned into a union that "really works" - not a European Commission of 28 Commissioners, but a smaller kind of governing body consisting of only 12 members, boasting its own border patrol guards and army.
Whatever the outcome of the referendum may be, the EU should take an assertive position, Verhofstadt said.
If the UK stays, it cannot renegotiate terms again, the former Belgian Prime Minister argued. This means the UK can't stop the EU from going towards an ever closer union.
"But out is out" and no new negotiations will follow, he said.
Elsewhere, the Belgian financial daily L'Echo reports that British businesses based in Belgium are running scared about the outcome of the poll and fear that the country could leave the EU.
The daily says that practically all British businesses based in Belgium are hoping for a 'Remain' outcome on Thursday.
Glenn Vaughan, the CEO of the British Chamber of Commerce in Belgium, said, "It's clear that being part of the EU is essential for the UK and investments. 97 per cent of our members wish to remain in the EU."
He warned that leaving the EU could mean a return to export tariffs and complicated paperwork.
The Chamber represents 250 businesses active in Belgium and includes the pharmaceutical giant GlaxoSmithKline (GSK).