Halifax said house prices rose by 0.6 percent in May, twice the rate forecast in a Reuters poll of economists and largely reversing April's 0.8 percent dip.
"The strength of demand, combined with very low supply, is causing house prices to rise at a brisk pace," Halifax housing economist Martin Ellis said.
Prices in the three months to May were 9.2 percent higher than a year earlier, the same rate of increase as in April, which was the slowest since November. Bank of England mortgage data for April showed the weakest net lending growth since the depths of the euro zone debt crisis in 2012, and the sharpest fall in mortgage approvals in two years.
Halifax house price data typically shows a faster rate of price rises than other measures. Rival mortgage lender Nationwide reported a 4.7 percent annual rise in prices for May.
The Royal Institution of Chartered Surveyors reported the biggest fall in demand from buyers since 2008 last month, Halifax's Ellis said he expected price rises to slow later in 2016 as price rises continued to outpace earnings growth.
"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," he said. Halifax did not refer to Britain's June 23 referendum on EU membership, which has reduced demand for commercial property.
(Reporting by David Milliken; Editing by Sarah Young and Hugh Lawson)