The think tank Centre for Economics and Business Research (CEBR) predicts the UK economy will outstrip France and Germany within two decades even if Britain stays in the EU.
But while leaving the organisation would have initial negative consequences, the CEBR's chief executive Douglas McWilliams suspects "that over a 15-year period, it would probably be positive."
Britain is set to vote on a referendum on EU membership in 2017.
The report predicts the UK's GDP will first move to fifth place ahead of France by 2018 before leapfrogging Germany around 2030.
However, despite being forecast to be the second most successful of the Western economies after the US, it will fall behind the accelerating economies of India and Brazil.
"Germany is forecast to lose its position as the largest Western European economy to the UK around 2030 because of the UK's faster population growth and lesser dependence on the other European economies," the report said.
But added: "If the euro were to break up, Germany's outlook would be much better.
"A Deutsche Mark-based Germany certainly would not be overtaken by the UK for many years if ever."
It added that a factor driving the UK's move ahead of Germany is the assumption of a falling value for the euro, Germany's falling population and the UK's rising population.
The gap between the two countries will fall from almost £610billion in 2013 to just £183billion in five years.
The UK's GDP will grow from more than £1.59trillion in 2013 to £2.6trillion in 2028, compared to China which is predicted to be in top position with a GDP of more than £20.5trillion, ahead of the US with an estimated £19.7trillion
Japan will fall from its steady position in the global league of third to fourth by 2028, overtaken by India and followed by Brazil, Germany and the UK.
The positive report on the economy comes as a poll reveals more people believe they would be helped rather than harmed by a rise in interest rates.
A survey reveals that a pre-election rate hike could actually improve David Cameron's chances of staying in Downing Street, rather than damaging them, as is widely thought.
Some 31 per cent of those questioned by YouGov for The Times said that a rise in interest rates would leave them personally better-off, against 23 per cent who said they would be better-off with lower rates and 32 per cent who thought it would make little difference either way.
Faster than expected recovery has prompted speculation that the Bank of England's Monetary Policy Committee may increase the base rate from its historic low of 0.5 per cent before the general election in May 2015.
The Bank's Governor Mark Carney has previously said that he does not expect a rise until unemployment drops to 7 per cent, probably in 2016. But with official jobless figures now standing at 7.4 per cent, many observers believe the crucial figure may be hit as early as next year.
A rise in interest rates would hit mortgage-holders, making it more difficult for home-owners to pay back loans. But it would be good for savers, particularly pensioners who have suffered from poor rates of return on their nest-eggs over the period since the crash of 2008.
YouGov president Peter Kellner told The Times: "For the moment, when inflation looks set to stay low, a modest rise in interest rates is actually likely to please far more people than it troubles.
"In electoral terms, that effect is likely to be heightened as the very people who plainly benefit most from rising rates - the over-60s - are those most likely to vote.
"If David Cameron and George Osborne can preside over low consumer-price inflation but higher rises in the price of homes and other assets such as shares, then some rise in interest rates is likely to win them more votes than it loses."