House prices rose by just 0.1% in May, the smallest monthly increase since January, the Halifax bank said.
May's rise was markedly below the 2.0% increase recorded in April. The annual rate of price increase stands at 9.1%.
"There are signs that housing market activity may be beginning to level out," Martin Ellis, Halifax chief economist, said.
Significantly higher household bills and rising unemployment lie at the heart of the slowdown, Halifax said.
The bank pointed to a number of key indicators of a slowing housing market.
These included Bank of England figures showing a fall in the number of new mortgage approvals, and a survey from the Royal Institution of Chartered Surveyors which found the number of agreed property sales were virtually unchanged.
The 0.1% rise recorded by the Halifax is in line with the latest survey from the Nationwide Building Society's survey which said that prices rose by 0.2% in May.
GOT A PROBLEM?
Locking horns with a firm or government agency? Got a different kind of personal finance or consumer affairs problem?
Send your story to our team of journalists, and we will investigate.
E-mail us on email@example.com
Subject field must say BBC Your Money
Please supply daytime contact number
Halifax predicted that the housing market activity would continue to "level out" during the second half of 2006.
The bank's view of future price growth was cautiously supported by Howard Archer, chief UK economist at Global Insight.
"There are growing signs that the recent 'mini boom' in the housing market is faltering," Mr Archer said.
"Consequently, we are becoming modestly more confident in our long-held belief that house prices will ease back into an extended period of relatively modest rises over the coming months," he added.