The January figure is up from the £7.3bn recorded for approved mortgage loans in December, but is markedly down by 59.4% from the previous year.
House purchase loans were up marginally at £2.9bn, from £2.7bn in December.
The January figure is down 56.1% from the same time last year.
Gross mortgage lending remained flat at £9.9bn, a decline of 45.2% from January 2007.
Net mortgage lending rose by £2.9bn in January, compared to £3.3bn for the previous month.
Despite this, annual growth for net mortgage lending is up 10%.
Personal deposits fell by £2.3bn as a result of savers seeking alternative deposit products.
David Dooks, statistics director of the BBA, says: “The high street banks’ mortgage lending is still seeing double-digit annual growth, albeit in a much slower market.
“Lower borrowing costs and falling property prices have underpinned demand at these lenders, who are providing over two-thirds of all new mortgage lending.”
He adds: “There is only limited demand from households for unsecured credit, while a fall in their deposits in January reflects a tendency to draw on cash or to move into alternative financial products.”