The Halifax has reported that annual rate of growth in May was unchanged at 9.2%, the lowest since last autumn.
House prices in the three months from March to May were 1.4% higher than in the preceding three months.
The monthly change was an increase of 0.6%.
The Halifax said the average price of a home during May was £213,472.
Martin Ellis, Halifax housing economist, said: “Low interest rates, increasing employment and rising real earnings, continue to support housing demand. The strength of demand, combined with very low supply, is causing house prices to rise at a brisk pace in quarterly and annual terms.
“Increasing affordability issues, caused by a sustained period of higher-than-earnings house price growth, should curb housing demand and result in some slowdown in house price growth as the year progresses.”
Ian Thomas, director of LendInvest, added: “The resilience of house price growth is remarkable. Even now that the stamp duty stampede of the first quarter is behind us, and with the uncertainty of the EU referendum result dampening activity, house prices are still holding up.
“Demand continues to outpace supply; there simply aren’t enough houses being built. The latest disappointing housebuilding stats make this abundantly clear. The government’s dream of one million new homes by 2020 simply isn’t realistic without a fundamental change of approach.
“As a result, house prices will continue to rise. Investors will continue to enjoy great returns from putting their money into property, while aspiring home buyers face a tricky time getting the sums to add up in order to move up the housing ladder.”