It says that all forms of mortgage approvals weakened in March and are now at their lowest since September 2000.
The number of house purchases dropped from 43,147 in February to 35,417 in March.
This is a drop of 46.2 per cent from the same time last year.
Remortgages also dropped from 69,997 in February to 60,503 in March. This was down 7.9 per cent from the same time last year.
Approvals for remortgaging represented nearly 50 per cent of total approvals.
The BBA says that gross lending totalled £16.6bn in March, down from £17.6bn in February.
BBA statistics director David Dooks says: “The consequences of low banking sector liquidity show up clearly in March data; reduced product ranges and tighter criteria resulted in slower mortgage lending and significantly fewer loan approvals. Pressures on personal finances are also constraining demand, not only for mortgages, but also for personal loans and borrowing on cards.”