The growth is at its fastest pace since June 2007.
The level of business was also seen as being normal after being regarded as below normal since September 2007.
And in the next three months firms expect business to continue growing said CBI/PwC.
Of the 106 financial companies surveyed 53% saw volumes rise in the quarter to December and 24% reported a fall.
The resulting balance of +29% is the highest since June 2007 and above expectations. Firms expect volumes to continue to increase next quarter at 19%.
Optimism in financial services was lower than three months ago, down by 24% and employment was also down 13% with firms predicting an 18% decline next quarter.
Companies say they will invest less in land, buildings, vehicles, plant and machinery over the next year.
Firms also said they planned to invest less in marketing over the same period representing the first fall since September 2009.
Investment in information technology is expected to see a minimal increase of 4% which is well below its long-run average of 28%.
Shortage of finance, uncertainty about demand and business prospects and inadequate return on investment were seen as the factors most likely to limit investment.
Ian McCafferty, chief economic adviser at the CBI, said: “This has been a strong quarter for the financial services sector with increases in sales volumes and profits showing that the sector’s recovery is on track.
“But firms are less optimistic, employment is down and investment intentions for next year are weaker, as concerns about the global recovery and ongoing troubles in the eurozone create uncertainty.
“Nevertheless companies are expecting business volumes and profits to continue to grow, albeit more slowly, in the next three months.”
