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%."
10 property hotspots
10 property hotspots
In Scotland, Edinburgh is seen as a city with huge growth potential. In 2014, prices in Edinburgh were up 10% in a post referendum boom that shows little sign of slowing down.
Local agents are not expecting quite such stellar growth for the next 12 months, but they think price rises will be well above the average predicted for the whole country.
Rightmove named this as the area where it expects house prices to grow the most over the next five years. It says that over this period there will be a huge number of people moving out of London in order to afford to get onto the property ladder. They want a reasonable commute combined with plenty of attractions in the local area, and Southampton offers all this. With relatively affordable housing stock, it's a prime candidate for growth.
Luton was Rightmove's candidate for the second biggest house price rises over the next five years. It emphasised that this isn't a mater of opinion, it is the result of crunching the data.
Luton is another major beneficiary of the move out of London, and while it is arguably not as attractive a place to live as Southampton, it's only 23 minutes into central London - which rivals some of inner London's commuter times. With average prices of £179,368, it's clearly a far more affordable option, and the area has already started to show signs of a boom.
This was the third area suggested by Rightmove. As with Southampton, it is well positioned for London commuters, and also has huge local attractions.
A survey last year asked young professionals to name the place they would most like to live, and Brighton and Hove were the only areas that appeared on the list outside London.
One of the reasons it's not higher up the list is that houses are already on the pricey side, with an average cost of £338,956 - up 13% in the past year alone.
There may be few people who grow up with the dream of living in Swindon, but the electrification of the rail line to London will bring travel times down across the West Country, so Swindon becomes part of the outer commuter area.
Given that the average property costs £168, 968, it's easy to see why Swindon will be a popular option for commuters on a tight budget.
Bath is also going to benefit from electrification of the line, because the commute to London will fall to a manageable 70 minutes. The beauty of the city - along with a vibrant social and cultural life - makes it a clear choice for more long-distance commuters.
Of course, with an average asking price of £374,617, it's not a tremendously cheap place to buy, but the geography of the city restricts development, so these prices are expected to rise still further.
Property Frontiers says that the booming house prices in Oxford are set to get even higher. At the moment, travel to London takes 60 minutes, but this will reduce even further in 2016 when the line is electrified. Prices in the most desirable parts of the centre aren't much cheaper than London.
However, further out there are pockets of affordability, and when the Water Eaton station opens in 2015 it will open up areas to the north of the city too.
Manchester has seen enormous property price rises over the last couple of years, and Property Frontiers expects this to continue into 2015.
Other commentators are expecting the growth to slow over the next few years, especially given the gains made since 2012. However, demand for properties remains buoyant, and with the growth of the local economy, price rises seem inevitable.
Rising prices in London have pushed buyers further and further out of the centre, so estate agents are now claiming zone three as 'the new zone 2'.
Savills believes that the biggest gains over the next five years will be the less glamorous districts - putting the South and East in the frame. Gritty areas that could benefit include Ladywell, Streatham and Catford in the south, and Leytonstone, Forest Gate and Walthamstow in the east.
Cambridge could also perform well. It has already had house prices lifted by the growth of tech companies to the north of the city, and the arrival of pharmaceutical headquarters will help push prices up further.
In 2016 a new rail service from the city to the science park will keep prices rising, and beyond the opportunities presented by the local economy, Cambridge is also part of the 'outer commute' area of London, which Savills expects to shoot up in value over the next five years.