But housing experts are keen to stress that this is not the beginning of a house price explosion.
Brian Davis, Nationwide's operations director, said: 'A recovery in the housing market does appear to be under way, but it is still fragile with turnover still only slightly above last year's depressed levels.'
House prices, according to Nationwide, are 3.5 per cent below those of a year ago. But last month's rise was the fourth consecutive month in which prices have risen, with a 3.5 per cent increase in total since May.
The average house in the United Kingdom is now worth pounds 53,710 - pounds 844 more than in May.
The Halifax Building Society house price index, which recorded a fall of 1.2 per cent in May, is due out next week. It is not likely to show such a dramatic price rise for June. But Halifax economist, Gary Marsh, said demand was picking up, with June bringing out more buyers.
Confidence in the state of the housing market rose last month according to a Gallup survey.
In June, for the first time since the survey began, homeowners began to believe that they would find no difficulty in selling their homes.