House prices are now increasing at around half the yearly rate they were six months ago, according to an index.
Property values in September were up by 5.8% annually, marking a cooldown compared with a 10% rate of annual price growth recorded just six months earlier, in March.
Halifax, which released the figures, said September's 5.8% yearly growth rate was the weakest recorded since August 2013.
On a monthly basis, prices edged up by 0.1% in September, following two months of price falls. The average UK house price in September was £214,024.
Martin Ellis, a housing economist at Halifax, said: "The housing market has followed a steady downward trend over the past six months, with clear evidence of both a softening in activity levels and an easing in house price inflation."
He continued: "A lengthy period where house prices have risen more rapidly than earnings has put pressure on affordability, therefore constraining demand. Very low mortgage rates and a shortage of properties available for sale should, however, help support price levels over the coming months."
Halifax said quarterly changes in house prices tend to be a more reliable indicator of what is happening in the market than monthly changes.
On a quarterly basis, house prices in the three months to September were 0.1% lower than they were between April and June. This was the weakest quarterly rate of change seen since November 2012.
Jeremy Leaf, a north London estate agent and a former residential chairman of the Royal Institution of Chartered Surveyors (Rics), said Halifax's figures indicate house prices "held up better than expected", considering they reflect the months following the Brexit vote.
He said: "Since the beginning of September we have seen an increase in activity, although buyers are still relatively slow to commit until they are sure they have achieved what they think are the best possible terms."
Mark Harris, chief executive of mortgage broker SPF Private Clients, said: "Despite the uncertainty and concern surrounding the referendum, the market seems to have quickly absorbed the ramifications of the UK's decision to leave the EU.
"We were concerned that Brexit would mean the market would stall, with buyers and sellers racked with indecision, but that doesn't seem to have happened. It certainly helps that mortgage rates are so cheap and it looks as though we will be in an extremely low interest rate environment for the foreseeable future, so there is great value to be had."
Howard Archer, chief UK and European economist at IHS Global Insight, said Halifax's figures reinforce his belief that house prices will be "essentially flat" over the final months of 2016.
He said: "While softer housing market activity is likely to limit house prices, we suspect that the current resilience of the economy and a shortage of properties will prevent prices from falling over the final months of 2016."