House price growth is running at around a third of the levels seen in spring last year, according to an index.
Property values increased by 3.3% annually in May, the lowest annual rate since a 2.6% increase in May 2013, Halifax said.
The 3.3% increase is around a third of a 10% rise in March last year.
There has been "virtually no change" in house prices over the last three months, Halifax said. Property values increased by 0.4% month-on-month in May, to reach £220,706 on average across the UK.
Martin Ellis, a housing economist at Halifax, said: "The fact that the supply of new homes and existing properties available for sale remains low, combined with historically low mortgage rates and a high employment rate, is likely to support house price levels over the coming months."
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said May's Halifax data should allay concerns that house prices are on a downward spiral.
He said: "Admittedly, average prices still are 0.7% below their December 2016 peak, but Halifax hasn't reported a month-to-month decline in prices since January.
"Recent further falls in mortgage rates are helping home buyers to take out slightly larger loans, even though their real wages are falling.
"In addition, prices are being underpinned by a sharp reduction in supply. The extremely low rate of job losses means that few home owners are being forced to sell their homes and many are deciding to delay listing their homes until the market strengthens again.
"So, while the days of rapid house price growth fuelled by sharp increases in leverage are over, we still see scope for prices to edge up over the rest of 2017."