This is according to the latest Nationwide House Price Index.
Commenting on the figures, Robert Gardner, Nationwide's chief economist, said: "House prices increased by 0.3% in May, only just offsetting the 0.2% fall recorded the previous month, and leaving prices 1.2% below the level prevailing in May 2010.
"At 0.6%, the three month on three month measure of house prices was little changed from the 0.7% pace of increase recorded in April.
"Overall, the modest pace of house price growth in May suggests that the property market is continuing to mirror the lacklustre trends evident in the wider economy.
"The UK economy returned to growth in the first three months of 2011, albeit at a modest pace, with business surveys suggesting that growth has been maintained in Q2. Employment has also edged up in recent months, and housing affordability, as measured by the house price to earnings ratio, is not as stretched as it was in the run up to the financial crisis.
"Nevertheless, the modest improvement in economic conditions has so far been insufficient to pull the housing market out of its torpor, as the headwinds facing households remain strong.”
Commenting on the Nationwide data, Simon Rubinsohn, RICS chief economist, said: “The Nationwide data on house prices released this morning provides further evidence of a largely stagnant residential market.
“This follows on from numbers on the level of transactions published earlier in the week by the HMRC and the BBA, both of which showed a broadly flat trend in sales.
“Meanwhile the forward looking indicators from the last RICS Housing Market Survey suggest that there is little reason to expect an improvement in turnover in the near term. A combination of factors including uncertainty over the outlook for the economy and an ongoing reluctance from the banks to make finance more readily is continuing to cast a pall over the sales market.
“This would matter less if the availability of rental property, whether privately let or social, was increasing. The upward pressure on rents is a clear indication that this is not the case. Indeed, reforms to financing arrangements for social housing raises significant doubts as to whether new provision can keep pace with need.
“Although the mood music in government does seem to have shifted more in favour of development in recent months, it is absolutely critical that the rhetoric feeds through into actions. Failure to act is likely to result in the cost of all tenures of housing continuing to rise.”
