Lenders reported that this was the third successive quarter of falling demand, the bank's Credit Conditions Survey found.
Mortgages for high-value property saw the biggest fall in demand since the third quarter of 2008.
Demand was expected to bounce back in the second quarter.
Some lenders attributed the fall in demand over recent quarters to a combination of changes in regulatory policy and concerns about housing affordability, as well as uncertainty about the outlook for the housing market.
However, the predicted recovery might point to the effect of the general election campaign on the UK housing market.
"For demand to have fallen particularly sharply at the upper end of the market underlines the sensitivity of this demographic to political uncertainty," said Jonathan Samuels, chief executive of Dragonfly Property Finance.
"Many prime and super-prime buyers are sitting on their hands and want to see what the next government looks like before they commit to a purchase. That this is the most uncertain election in decades has certainly triggered more caution at this level of the market than normal."
The survey suggested that lenders were showing a greater willingness to lend to borrowers who were only able to offer a deposit of less than 10% of the property's value so far this year. Many of these borrowers would be first-time buyers.
Demand for mortgages fell sharply in the first quarter of the year in the UK, according to research for the Bank of England.