The number of mortgages approved for house buyers was down 16% in October compared with last year, at just over 37,000, according to the British Bankers Association.
High house prices and tougher rules on mortgage applications appear to be holding buyers back.
Matthew Pointon of Capital Economics commented that the figures reflect a "sharp slowdown in housing demand", though a flurry of cheaper mortgage deals could revive interest.
The Halifax predicted that overall growth in house prices would slip to between 3 and 5 per cent next year, after peaking at 10 per cent in July.
However, the number of house sales is still on the up according to data from HM Revenue & Customs, which takes into account purchases for cash as well as mortgages.
HMRC reported on Friday that there were 114,000 transactions in October, a rise from 102,000 in the same month last year.