House prices have been rising modestly on this three month-on-three month measure since December 2012 with increases of between 1% and 2% in each of the past five months.
Martin Ellis, housing economist, said: "House prices continue to pick up gradually. Prices in the three months to May 2013 were 1.5% higher than in the preceding three months. This was slightly higher than the 1.3% increase in the three month-on-three month measure in April.”
Prices in the three months to May were 2.6% higher than in the same three months a year earlier, which was the biggest increase since September 2010.
In the month of May house prices increased by 0.4%, the fourth consecutive monthly rise.
And the index showed a modest pick-up in home sales and improvement in market conditions since late 2012.
Home sales in the three months from February to April were 2% higher than in the preceding three months despite a 5% decline between March and April.
Meanwhile the ratio of house sales to the stock of unsold properties has increased since last autumn. This evidence of strengthening in demand relative to supply helps to explain the modest rise in house prices over recent months.
Ellis added: "Despite these recent signs of improvement in the housing market the subdued economic background and the accompanying weak income growth continue to be a significant constraint on housing demand and activity."
Brian Murphy, head of lending at Mortgage Advice Bureau, said: “The property market’s sunny disposition continues this month as Halifax reports the greatest year-on-year increase since 2010 for property values in May. Outstanding fixed rates are brightening buyer’s prospects in the market and feeding enthusiasm for bargain mortgage deals.”
And Karelia Scott-Daniels, managing director of buying agents Manse & Garret Property Search, said: “Consumers are still cautious but they are considerably less cautious than they were two to three years ago.
“Improved mortgage availability, lower loan rates and relaxed criteria have certainly contributed to the rise in house prices. As ever it's important to remember that the overall figure does not reflect the fact that many local markets, especially in the North, are struggling.”
Jonathan Hopper, managing director of property search consultants Garrington, cautioned against viewing the market as rosy because of consistent growth.
He said: "In reality there are two distinct markets out there - London and the South East, and the rest of the country.
"In the capital house prices are rising at a rate of knots and in some boroughs there has been a return to sealed bids.
"But in many areas across the UK, sellers are having to cut their prices to tempt buyers and less desirable properties are languishing on the market for months.”