This growth was marginally lower than in the second quarter and in the corresponding quarter of 2007.
Over the twelve months to September loans grew 10% to £44.8bn, while overdraft borrowing stood at £9.3bn, some 4% higher than a year earlier.
Total deposits totalled £55.0bn, 3% up on the year.
New banking relationships have been established for 538,300 small businesses.
BBA statistics director, David Dooks, said: "The effects of the deteriorating economy are becoming more apparent. Slowing growth in deposits shows that small businesses are increasingly funding their activities out of cashflow, but a rise in lending in the third quarter, consistent with growth in the previous quarter and the corresponding quarter of 2007, shows banks continuing to make finance available."
