The survey of five European countries by TNS found 78 percent of Germans, more than two-thirds of Spaniards and almost six out of 10 French wanted Britain to stay in the EU.
That far outstripped the 38 percent of Britons who backed staying in the union, only slightly more than the 34 percent who want to leave, according to TNS. Some 28 percent were still undecided.
The question will be put to a referendum on June 23rd, when the British public will vote on whether to stay part of the 28 member European Union or strike out alone.
The issue has split the British government, with Prime Minister David Cameron facing viscious opposition from senior figures in his own party such as Justice Secretary Michael Gove and London Mayor Boris Johnson.
Brits currently expect the 'In' camp to win it - 40 percent expect Britain to stay in the EU, according to Wednesday's survey, compared to 26 percent who expect voters to back leaving.
Produced by Le Figaro from findings by TNS
Their European counterparts were more optimistic, with 47 percent of Germans, 48 percent of Spaniards and 44 percent of Poles predicting Britain will avoid an exit.
Only in France did more people expect Britain to go than not, with 52 percent predicting a Brexit and 48 percent saying the referendum will back staying.
Asked about the consequences of of leaving, only a tenth of Brits said the EU's economy would improve while 38 percent it would deteriorate and 21 percent said nothing would change.
Their continental counterparts were less hopeful, however. Two-thirds of Germans, 43 percent of Spaniards, 39 percent of Poles and 33 percent of French predicted a Brexit would hurt the EU's economy.
The survey, carried out by TNS between April 4-14th simultaneously in France, Germany, Spain, Poland and Britain, was published in French media on Wednesday.