House prices dipped by 0.2% month-on-month in August amid signs of softening sales activity, Halifax has reported.
The monthly decrease is smaller than a 1.1% price fall recorded in July, and took the average UK house price last month to £213,930.
Property values were still 6.9% higher than a year earlier - although this was the lowest rate of annual growth seen since October 2013.
Year-on-year price growth had been running in double digits earlier this year, with a 10% annual upswing recorded in March.
Halifax said the quarterly house price growth rate is often a good indicator of underlying housing market trends.
On a quarterly basis, house prices in the three months to August were 0.7% higher than in the previous quarter, down from 1.5% in July.
Martin Ellis, Halifax housing economist, said: "House price growth continued the trend of the past few months in August with a further moderation in both the annual and quarterly rates of increase. There are also signs of a softening in sales activity.
"The slowdown in the rate of house price growth is consistent with the forecast that we made at the end of 2015.
"Increasing difficulties in purchasing a home as house prices continued to increase more quickly than earnings were expected to constrain demand, curbing house price growth."
At the end of 2015, Halifax predicted UK house prices would increase by between 4% and 6% by the end of this year.
Several reports have painted a mixed picture of the housing market so far, following the vote to leave the EU.
Last week, in contrast to the Halifax, a separate index from Nationwide Building Society had put house prices as increasing by 0.6% month-on-month in August.
Nationwide said one of the reasons prices had held up while activity slowed down was a lack of homes on the market for buyers to choose from.
And this week, house builder Redrow brushed aside fears over the Brexit vote as it posted a record annual profit haul and predicted an "excellent" year ahead.
Jeremy Leaf, a north London estate agent and a former residential chairman of the Royal Institution of Chartered Surveyors (Rics), said: "On the ground we are not finding a huge change in prices, just a determination for buyers and sellers to get on with moving but at more realistic price levels."
Recent stamp duty changes have also shown signs of disrupting the market, with a three percentage point hike in the tax having been imposed on buy-to-let investors from April 1.
Howard Archer, chief UK and European economist at IHS Global Insight, said he expects house prices to be "essentially flat" over the final months of 2016.
He continued: "However, we still believe that a dip in house prices is likely in 2017, probably by around 3 to 5%."