Opponents of the euro say the pound is a key part of British sovereignty
A BBC poll has found that 71% of people would vote against Britain joining the euro if it were put to a referendum.
The survey of 1,000 adults revealed that just 23% would vote "yes" to joining the European single currency, while 6% said they were unsure.
Only 15% said the recent fall in the value of the pound against the euro made them more likely to vote "yes", while 69% said it made no difference.
Sixteen countries now use the euro, which was introduced 10 years ago.
Slovakia became the latest country to start using the currency on New Year's Day.
Recently the pound has plummeted against the euro and some have suggested that it could be time for Britain to join the single currency.
While at the beginning of 2008 a pound was worth 1.34 euros, it now only buys just over one euro.
But the BBC poll, for Radio 4's The World at One, appears to show that recent developments have done little to improve the euro's image in the eyes of ordinary voters.
The Europe minister, Caroline Flint, said a debate about joining the euro was a red herring, adding that changing currency would not solve the economic crisis.
"I actually agree with the people who took part in this opinion poll," she said. "It's not surprising to me... when people are facing problems with their housing, problems on the job front.
"Those are the first order issues we have to deal with, and changing the currency is not a solution to tackling the financial stability."
Similar surveys carried out by the BBC in past years show how the pattern of support for the euro has changed.
It was least popular in November 2000, when 71% were opposed to it and just 18% were in favour.
At its most popular in January 2002, 31% of people said they would vote "yes" to joining, while 56% opted for "no".
Last month, European Commission president Jose Manuel Barroso said the UK was "closer than ever" to joining the euro and that the "people who matter" in British politics were contemplating giving up the pound.
But Business Secretary Lord Mandelson said that while joining was still the government's long-term policy aim, such a move was "not for now".
Meanwhile, the shadow foreign secretary reportedly told the Daily Mail newspaper that the Tories under David Cameron "would never join the euro".
William Hague was quoted as saying: "A Conservative government under David Cameron would have no ministers telling Brussels we would be better off without the pound and no goal of joining the euro one day."
The BBC's political correspondent Gary O'Donoghue said Tory sources insisted the party's position on the single currency had not changed.
But our correspondent said that the Conservatives' most recent election manifesto had not used the word "never" with respect to the euro.
The UK Independence Party (UKIP), which wants Britain to withdraw from the European Union, burned a bundle of euro notes outside the Bank of England of Thursday to mark the single currency's 10th birthday.
Dr John Whittaker, UKIP MEP for the North West, said the credit crunch had now exposed the euro's "real weakness".
"While all economies are suffering, some eurozone countries are now in an impossible position," he said.
"What these countries need is lower interest rates and devaluation but, stuck in the euro, there is nothing they can do."
The poll was carried out by ICM between 19 and 21 December 2008.