British research group the Centre for Economics and Business Research (CEBR) predicts that Britain's output will outstrip France's by 2018 before displacing Germany by around 2030.
But it will be overtaken by India and Brazil over the same time period, the study said.
"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.
"If the euro were to break up, Germany's outlook would be much better," it added. "A Deutsche Mark-based Germany certainly would not be overtaken by the UK for many years if ever."
The think-tank's chief executive claimed that Britain's economy would grow even faster if it left the European Union.
"My instinct is that in the short term, the impact of leaving the EU would undoubtedly be negative," Douglas McWilliams told the Daily Telegraph. “My suspicion is that over a 15-year period, it would probably be positive."