Research found the sector, which employs more than 50,000 people, reported its fourth consecutive year of growth in 2012 and had expanded by 6.5% when compared to 2011.
According to TheCityUK fund management report, around £2tr of the funds came from overseas clients with the US the biggest source.
Two-thirds were from institutional clients, retail clients made up a further 14% with the remainder coming from private client or alternative funds.
The researchers estimated assets have increased nearly 5% in the first nine months of 2013 with the full-year rise expected to be around 7%.
The UK accounts for more than 8% of global fund management assets.
Chris Cummings, chief executive of TheCityUK, a financial services membership group which promotes the industry, said: "The UK is one of the most open markets in the world for fund management.
"UK firms are also well positioned to gain new international business, particularly in emerging markets where growth prospects look strong.
"The UK Government is committed to ensuring the UK remains an open and competitive market for international investment.
"While London is central to the UK's strong international position, other cities such as Edinburgh, Glasgow, Aberdeen, Manchester, Liverpool, Cardiff and Birmingham, are also important centres for fund management."