That is up from 9.9% in the previous month.
Once again, the market was in large part driven by London, where house prices rose by a record 20.1% over the year.
But excluding London and the South East, prices rose by a much more modest 6.4% across the UK.
Prices were up in every region, except for Northern Ireland, where they fell by 0.7%.
In England, prices rose by 11%, in Wales prices were up by 6.5%, and in Scotland they rose by 3.6%.
According to the ONS index, the average price of a house across the UK is now Â£262,000.
"Annual house price growth of 20.1% is borderline insane, but there are signs that the capital started to cool slightly in June and July," said Jonathan Samuels, the chief executive of Dragonfly Property Finance.
The housing charity Shelter said the only answer was more house-building.
"Once again these figures show that house prices are spinning out of control, putting a stable home even further out of reach for ordinary families," said Campbell Robb, Shelter's chief executive.
"Instead scores of people are either stuck in their childhood bedrooms or forced to bring up children in unstable and expensive rented homes, however hard they work or save," he said.
Annual house price inflation hit 10.5% in May, the highest rate for four years, according to the Office for National Statistics (ONS).