Prices were up 1.3 per cent in June as compared to May, according to the Halifax House Price Index, which recorded data throughout the month - giving some measure of changes to prices after the Brexit vote.
However, year-on-year growth was at 8.4 per cent, falling from 9.2 per cent in May, suggesting the market may be easing off.
On a three month analysis, Halifax found the growth rate had fallen from 1.4 per cent in May to 1.2 per cent in June. This figure was 1.5 per cent in April, 2.9 per cent in March and 3.0 per cent in February.
Martin Ellis, Halifax housing economist, said: "There is evidence that the underlying pace of house growth may be easing."
"House prices continue to increase, albeit at a slower rate, but this preceded the EU referendum result, therefore it is far too early to determine any impact since."
Howard Archer, chief UK economist at IHS, said: "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."
"This is likely to weigh down markedly on economic activity and consumer confidence, which is not good news for the housing market. Unemployment could also well rise over the coming months."
"We suspect that house prices could fall by five per cent over the second half of 2016 and there could well be another five to seven per cent drop in 2017."
Jeremy Duncombe, Director, Legal & General Mortgage Club, said:
As predicted, house prices have eased slightly in the weeks leading up to the EU referendum. However, we will only start to see the true shape of the new landscape when next month’s indices are released.