The figures showed the number of mortgage approvals experienced a slight increase from 37,241 in August to 38,252 in September.
However, the number was 15% lower than the same time last year, while the first nine months of 2016 saw a three per cent dip in approved mortgages compared to September 2015.
Remortgaging figures were similar to the same time period in 2015, but was 15% higher in the first nine months of 2016.
Gross mortgage borrowing of £12bn in September was two per cent lower than this time last year, while net mortgage borrowing was 2.6% higher than it was in September 2015.
The figures were driven by a strong demand for personal loans and credit cards.
BBA chief economist Dr Rebecca Harding said: “Consumers are increasingly using short-term borrowing to take advantage of record low interest rates. This trend has accelerated since the Bank of England cut rates in August.
“Mortgage approvals picked up slightly this month but the housing market continues to shows signs of underlying weakness.”
Jeremy Leaf, former RICS residential chairman, said the figures showed 2016 to be a year of two halves.
He advised that the market had not collapsed in the wake of the referendum vote but encouraged buyers and sellers to be pragmatic and demonstrate resilience during this period of uncertainty.