There were 64,645 mortgage approvals for house purchases in April, the Bank of England said, a 2% fall on the previous month.
Mortgage lenders have told of a fall in demand, despite the low rates on offer.
One theory is that landlords might have brought forward purchases, to avoid the latest in a series of tax changes.
From 1 April, the amount of tax relief they could claim on mortgage payments was reduced.
The Bank of England figures also reveal that it continues to be difficult for savers to get a decent return. The interest paid on variable Individual Savings Accounts (Isas) averaged 0.39% – a new record low.
Interest paid on instant access savings accounts was just above a record low.
Meanwhile, the rate of growth of consumer credit – such as credit card borrowing, loans and overdrafts – remained at more than 10% a year in April.
Authorities, including the Bank, have said they remain vigilant over these rising unsecured debt levels.