"The overall month-on-month decline has slowed to its lowest since February and in London there was modest house price growth for the first time since January."
Prices are up by 2.1% on an annual basis, rising from 1.8% in May, led by the North East which saw annual growth of 3.7%.
That makes the average house in England and Wales in June worth £303,960 – up more than £6,000 on last June.
London saw modest house price growth for the first time since January, but although Greater London is the only region to have seen growth accelerate, it is far from being the strongest performer.
On a monthly basis average prices in England and Wales were slightly down in June, falling by 0.2% from May, although this is a smaller decline than March or April.
Oliver Blake, managing director of Your Move and Reeds Rains, said: “Two key factors could give rise to cautious optimism this month. The overall month-on-month decline has slowed to its lowest since February and in London there was modest house price growth for the first time since January.”