Seven out of 10 regions of England and Wales recorded month-on-month falls in house prices in June, according to the Land Registry.
Prices overall across England and Wales were unchanged in June compared with May, the survey suggested.
However, property prices were still 6.4% higher compared with a year ago, leaving the average home priced at £172,011.
A number of surveys have shown big annual price rises in recent months.
Surveys are now starting to make annual comparisons with a time a year ago when the housing market was firmly in the realms of recovery.
The latest Land Registry data shows that the biggest month-on-month rise in June was in the West Midlands (up 1.9%), with the largest fall in Yorkshire and the Humber (down 1.3%).
The largest year-on-year rise was in London (up 16.4%) and the slowest rise was in the North East of England (up 0.8%).
Other surveys in recent months have echoed the view of local markets moving at a different pace, but, overall, showing some levelling off of property prices.
A number of commentators have predicted a slowdown in the UK housing market during the summer holiday season, following the typical "Spring bounce" in activity.
