The increase from April to May was 0.9 per cent.
Of the 13 regions covered by the Office for National Statistics (ONS) figures, the biggest price increases were in the North West at 15.2 per cent, Wales with 13.3 per cent and Scotland, 12.1 per cent.
The lowest average price growth was in London at 5.2 per cent, then Northern Ireland at 6.0 per cent and East of England, 6.9 per cent.
First-time buyers paid 9.5 per cent more over the year and 0.7 per cent more month-on-month, with the average price £213,336.
For a former owner occupier, average price rises were 10.7 per cent yearly and 1.1 per cent monthly, with the average price tag £296,872.
Price increases on new builds outpaced rises on existing housing stock. For a new-build property, average price growth was 12.2 per cent annually and 5.1 per cent monthly, to £325,483.
Existing stock prices increased by 9.7 per cent over the year and 15 per cent month-on-month, to £251,199.
Mark Harris, chief executive at mortgage broker SPF Private Clients, said: “Continued strong demand for property, combined with a lack of stock, is pushing up prices further still.”
Nitesh Patel, strategic economist at Yorkshire Building Society, added: “Demand is strongest in areas of better affordability, namely the north.”
Nigel Purves, chief executive at Wayhome noted that for first-time buyers, “growth continues to exacerbate affordability concerns.”
Tomer Aboody, director of property lender MT Finance, added: “Buyer confidence remains high, in terms of the desire to move and in respect of getting the necessary finance approved, which is helping to push up prices.”
The overall 10 per cent price growth figure was driven by terraced houses at 11.4 per cent and detached homes at 11.3 per cent.
Price growth was lower for a semi-detached property price at 9.8 per cent, and for a flat or maisonette at 6.5 per cent.
The data for volume of transactions was not yet reliable because of the length of time taken to process deals, the report said.
However, comparing provisional estimates for March 2020 and March 2021, transaction numbers were up 71.1 per cent in England, 99.5 per cent in Scotland and 24.2 per cent in Wales.
The volume increase for property transactions Northern Ireland was 41.8 per cent in Q1 2021.