This doubling in size of assets that are now under U.K. regulation has put pressure on London to maintain its position in the global market, the FCA said.
"The survey illustrates how important this $2.6 trillion industry is to the UK. With nearly 20 percent of global assets under management here, it is important that people have confidence in how we regulate this market," said FCA director of supervision, Clive Adamson.
"As we move forward as the FCA, the challenge from us to the industry is to ensure that it operates to the highest standards of integrity so that London can maintain its position in this important global market," he added.
(Read more: Strauss-Kahn hedge fund aims to raise $2 billion)
The U.K.'s largest hedge funds are also growing, with 20 firms overseeing some 82 percent of the assets under management, the FCA said.
A vast majority of these funds are domiciled offshore, with 67 percent based in tax haven the Cayman Islands.
The FCA's survey primarily focuses on 106 funds from 49 firms, with $345 billion assets under management as of the end of September 2013.
(Read more: China-focused hedge funds buck market doldrums)
All the funds in the survey are at least partially managed by a U.K. regulated body and run by a single manager.
The 49 firms surveyed have assets worth a total of $481 billion, of which 43 percent or $206 billion is directly managed by staff a part of U.K. regulated bodies and their main place of business is the U.K.
The total number of global single hedge fund managers now sits at 8,000. Between them they work for 2,500 hedge fund management firms.
—By CNBC's Jenny Cosgrave: Follow her on Twitter @jenny_cosgrave