House prices are increasing at less than half the rate seen a year ago, according to an index.
Property values lifted by 3.8% year-on-year in March - compared with a 10% increase recorded in March 2016, Halifax said.
The latest annual increase is the weakest seen since a 2.6% rise in May 2013.
The average house price across the UK now stands at £219,755.
On a month-on-month basis, house prices have been at a standstill for two months in a row, with monthly growth of 0% recorded in both February and March.
Halifax's quarterly measure of house price growth showed that prices in the three months to March were 0.1% higher than they were between October and December 2016.
Martin Ellis, a housing economist at Halifax, said: "The annual rate of house price growth has more than halved over the past 12 months.
"A lengthy period of rapid house price growth has made it increasingly difficult for many to purchase a home as income growth has failed to keep up, which appears to have curbed housing demand.
"Nonetheless, the supply of both new homes and existing properties available for sale remains low. This, together with historically very low mortgage rates, is likely to support house price levels over the coming months."
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said Halifax's index adds to other recent reports as further evidence of a slowdown, adding: "It's now incontrovertible that the housing market has slowed sharply this year."
He said he expects house prices to increase by just 2% this year.
Mr Tombs continued: "House prices are being increasingly constrained by households' incomes, now that mortgage rates have hit a floor and regulations are preventing a further upward shift in average loan-to-income ratios."
The Centre for Economics and Business Research (Cebr) said this week that it expects house prices to keep pushing upwards in the coming years, despite uncertainty over Brexit. It said a continued lack of homes for buyers to choose from will help to underpin prices.
Cebr expects the average UK property value to increase by around £52,000 by 2021.
Jeremy Leaf, a north London estate agent and a former residential chairman of the Royal Institution of Chartered Surveyors (Rics), said: "What we have found on the ground is that there is more of a general acceptance that prices are flattening and if people want to move, then Easter is the time to get on with it and be more realistic about making and accepting offers."
Mark Harris, chief executive of mortgage broker SPF Private Clients, said: "Mortgage rates continue to stay low and competitive, which is helping support property prices to an extent.
"Even though swap rates have risen on the back of higher inflation, lenders seem willing to absorb some of the higher costs of funding, at least for now, in order to compete for business.
"This is good news for borrowers and those remortgaging as we head into what is usually the busiest time of the year for the housing market."