Average house prices increased over the year in England to £271,000 (9.7%), in Wales to £184,000 (13.3%), in Scotland to £171,000 (12.1%) and in Northern Ireland to £149,000 (6.0%).
Average house prices increased by 10.0% over the year to May, up from 9.6% in April, according to the latest figures from the ONS.
On a monthly basis prices were up 0.9% in the month to May to an average £255,000, nearly returning to the record average house price seen in March of £256,000.
Average house prices increased over the year in England to £271,000 (9.7%), in Wales to £184,000 (13.3%), in Scotland to £171,000 (12.1%) and in Northern Ireland to £149,000 (6.0%).
London continues to be the region with the lowest annual growth (5.2%) for the sixth consecutive month.
Tomer Aboody, director of property lender MT Finance, said: "Despite a dip in price growth in April, the housing market got back on track in May, continuing on its upwards trajectory.
"Buyer confidence certainly remains high, not only in terms of the desire to move but also in respect of getting the necessary finance approved, and this is helping push up prices.
"With so many mortgage products out there, buyers have the opportunity to get onto the property ladder, or move up it, at record low rates. If you have to stretch yourself to get a bigger mortgage to purchase the property you have set your heart on, low mortgage rates make this a much more palatable proposition.
"Stamp duty holiday or not, prime properties with good outdoor space, including room to work from home and not too far from the station or the office to make commuting possible where necessary, will always be in demand with multiple buyers willing, and able, to pay."
Mark Harris, chief executive of mortgage broker SPF Private Clients, added: "Continued strong demand for property, combined with a lack of stock, is pushing up prices further still. Low mortgage rates, combined with bigger deposits built up during lockdown, are giving buyers plenty of purchase power.
"Despite the tapering of the stamp duty holiday, there isn’t much sign of a significant slowdown in the market. Lenders remain keen to lend and interest rates look unlikely to rise anytime soon, resulting in some cheap mortgage deals, particularly for those with large deposits."