June’s figure is 34% higher than the average of the previous five months of £1.345bn.
The BSA found that mortgage approvals in June reached their highest level this year at £1.735bn, an increase of 11% on £1.559bn in May.
Net lending by mutuals for June was -£436m compared to -£661m in May.
Adrian Coles, director-general of the BSA, said: “Activity in the mortgage market has picked up compared to the start of the year and the rising number of approvals is a positive indicator for coming months.
“However, the forthcoming public sector cuts may add to the economic uncertainty, which could constrain any significant growth in mortgage lending in coming months.”