Fixed mortgage rates have fallen to new lows, but home loan approvals have also fallen to their lowest level since September.
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.