In a nationwide poll of 11,211 people aged 50 and over, 45% said they would vote to leave the EU.
Nearly two-thirds (66%) would prefer to have a referendum before the next general election, the Populus survey, conducted on behalf of Saga, also showed.
The poll, the largest of its kind, is also significant because older people are more likely to vote than any other age group.
Strategy director for Saga Group, Tim Pethick, said: "As the UK's political parties consider their commitment to a referendum and its timing, the nation's over 50s, who are the most likely to enter the polling booth, have spoken out.
"Saga's poll reveals an overwhelming desire for voters to have their say - and to have it sooner rather than later."
Saga provides a number of services to people aged 50 and over, including insurance, travel, healthcare and financial assistance.
The online survey found 45% would vote to leave the EU, compared with 33% who would vote to remain.
Some 65% of those polled believe a referendum should be held before the 2015 general election, compared with 35% who think it should wait until afterwards. The survey found 73% agree that an in/out referendum on Britain's membership of the EU should be held, compared with 27% who disagree.
Of those who believe a referendum is needed, 79% say one should be held before 2015, compared with 21% who say it should wait.
The older the voter, the more likely they are to have already made their minds up on which way to vote, according to the poll.
While 18% of those polled who were aged between 50-59 said their minds were not yet made up, the numbers decreased incrementally with just 12% of people in the 80-89 age group saying they were undecided.
Social class is also a deciding factor in determining support for either staying or leaving the EU, with 40% of the nation's highest earners/most comfortable pensioners saying they would vote to remain in the EU, compared to 61% of those in the lower earning categories favouring Britain find its own way outside the EU.
The majority of those in East Anglia would vote to leave the EU (53%), the next most Eurosceptic regions are East Midlands (49%), South West (48%) and Yorkshire & Humberside (48%).
Ukip leader Nigel Farage said of the findings: "In a poll of over 11,000 people the message is clear, people want their say. They don't want to wait for four years they want it now. A full 65% want to see the vote before the next general election.
"When they have their say it is also pretty clear that the majority of those who have made up their minds also want out."