Annual house price growth eased to 8.4% in the month of June, the lowest rate in a year, according to the Halifax, the UK's largest mortgage lender.
The quarterly rate of growth was 1.2%, the slowest since December 2014.
The pace of growth is still many times above general inflation, but one senior economist has warned of a "serious risk of an extended and marked downturn" following the Brexit vote.
The figures from the Halifax cover the period before the referendum result.
The annual rate is down from 9.2% in May.
"House prices continue to increase, albeit at a slower rate, but this precedes the EU referendum result, therefore it is far too early to determine any impact since," said Martin Ellis, Halifax's housing economist.
Howard Archer, chief UK economist at IHS Global Insight, said there was likely to be a major impact on house prices in the months ahead: "Despite the Halifax reporting a marked rise in house prices in June itself, we believe that the prospects for the housing market have deteriorated markedly following the Brexit vote.
"Housing market activity and prices now look to be at very serious risk of an extended, marked downturn following the UK's vote to leave the EU."
In the meantime the Halifax said the average price of a house has risen to another record high, at £216,823.
More homes for sale
An analysis by a firm of estate agents suggests that few buyers have backed out of house purchases since the referendum result.
Jackson-Stops and Staff looked at 750,000 properties for sale in the UK on Friday 24 June.
It found that 41% of homes on the market were already under offer.
A similar analysis on 6 July found that 39.9% were under offer - virtually the same proportion.
In addition, the number of properties for sale has increased by 21,000 since 24 June.