Average house prices increased by 0.2% between April and May, according to the latest figures from Nationwide.
The bank's House Price Index shows that annual growth slowed last month from 4.9% to 4.7%.
It calculates that the average UK house price in May was £204,368.
“The annual pace of house price growth remains in the fairly narrow range between 3% and 5% that has been prevailing for much of the past twelve months,” says Robert Gardner, Nationwide's chief economist.
“House purchase activity is likely to fall in the months ahead given the number of purchasers that brought forward transactions,” he adds.
Gardner predicts that the recovery thereafter may be gradual, especially in the rental sector, where policy changes, such as the reduction in tax relief for landlords from 2017, are likely to exert an 'ongoing drag'.
This week the Land Registry released its price paid data for April, which included the details of over 112,000 land and property sales in England and Wales.
Terraced properties accounted for the highest number of transactions, followed by flats and maisonettes.
The Land Registry says that just over 18,300 sales actually took place in April, 246 of which were for properties sold at £1 million or more.
The most expensive residential sale in April was a flat in Kensington and Chelsea for £6,250,000 and the cheapest was a terraced property in Bradford, sold for £14,100.
Last week haart's chief executive, Paul Smith, said he believed house price rises have now 'reached their peak'.
The agency urged sellers to be more realistic with the asking prices they're setting in the current market.