The increase is the largest rise in a single month since May 2007 when prices rose by 0.6%.
Hometrack said that a growth in buyer numbers combined with a scarcity of available property is also acting as a primary driver of price rises.
Richard Donnell, director of research at Hometrack, said: “House prices grew by 0.4% in May, the highest increase in a single month since May 2007.
“The impetus for rising house prices is originating almost exclusively from London and the South East where prices grew at an above average rate (0.9% and 0.5% respectively).
“Elsewhere housing market conditions are improving gradually with prices trending slowly upwards, averaging just 0.1% over May.
“While levels of demand for housing have been increasing each month, the total growth in buyer numbers has been broadly in line with that seen in recent years.
“But it is a lack of housing to buy that is driving the acceleration in prices. The shortage is being exacerbated by the rate of new stock coming to the market failing to keep pace with the number of sales agreed.
“Nationally, new supply grew by 2.8% in May while sales agreed were up 8.2%. Respondents to the survey reported a lack of housing for sale as one of their greatest concerns in the market at present with one reporting the lowest levels of stock for 15 years.”
In London the gap between supply and demand is the largest it has been since spring 2009. In the last six months demand has grown 15% while supply has declined by 0.6%.
Nationally the trend in prices is upwards with demand rising ahead of supply - albeit at a lesser extent than in London and the South East.
Prices remained static in four regions (North East, North West, Wales and Yorkshire & Humberside) and grew in a further four (East Anglia, East Midlands, South West and West Midlands).
Donnell added: “High moving costs, uncertainty over the outlook for jobs and a lack of available housing to move to means homeowners remain unwilling to put their own properties on the market. This is only serving to limit supply further.
“Talk of improving market conditions is likely to result in more marginal sellers entering the market in the coming months.
“The danger is that the pressure to secure instructions will lead to properties being put on the market at unrealistically high prices. This in turn will result in fewer sales and a period of price re-alignment.
“What we are seeing is the continuation of a series of small ‘mini housing cycles’ which have been in evidence over recent years.
“The improvement in market conditions is shown by a decline in the average time on the market to 8.8 weeks - the lowest level since July 2010.
“The sharpest falls in time on the market have been seen in Southern England while the time on the market remains around 11 weeks in the Midlands and Northern regions.
“The percentage of the asking price being achieved has risen to just under 94%, the highest level since July 2010.”
