The figure is broadly similar to the average of £2bn over the preceding three months.
Mortgage approvals fell by 8% in October to £1.8bn from £1.9bn in September.
Adrian Coles, director-general of the BSA, says: “Lending activity across the market has shown signs of weakening in recent months. Although lending by mutuals fell in October, gross lending remains similar to the average over the preceding three months.
“Reports of falling house prices and government spending cuts have lowered consumer confidence which has put further downward pressure on demand for mortgages.
“An encouraging trend in recent quarters, however, has been the growth in mortgage approvals at mutuals and this may lead to some recovery in mutuals’ market share over the next few months.”
Savings balances held at mutuals decreased by £1.1bn in October, following a decrease of £0.6bn in September.
Excluding interest credited to accounts £1.3bn was withdrawn in October, compared to £0.8bn in September.
Coles adds: “The current economic climate is proving challenging for households. Consumer price inflation remains above average earnings growth and the labour market remains fragile.
“This is squeezing household finances and many are using their savings to supplement their incomes or to pay off debt. The low interest rate environment is also proving a continued challenge to attract savings.”