The fire began at 14:00 at the Soho offices of the structured finance provider.
Reports say up to 50 people have been evacuated from the building.
Future Capital Partners has raised in excess of £6bn of investment since its launch in 2000.
The firm is one of the lead backers of wealth management platform Novia, which is headed by Bill Vasilieff.
A spokesperson for Future Capital says: “Future is pleased to report that none of its 40 staff was injured, and that is has suffered minimal disruption to its business. Due to the firm’s electronic data systems, back up and security policies, there has been no significant loss of material files and records, and the business continues to be fully operational..
“As of today, the firm and its staff have relocated to 271 Regent Street, London W1 and the main switchboard number is 020 7009 6600.”