UK house prices grew 3.7% compared to last year, in June, according to the ONS official house price data.
This annual growth rate is up from 2.7% in May, revised down from 3.9% previously.
In seasonally adjusted terms, prices rose by 0.9% month-to-month in June, up from a gain of 0.6% in May, with the successive bounces following the disruption to the market caused by the return of normal stamp duty rates in April.
Rates of house price growth continued to vary widely across the UK, with 7.8% growth seen in north-east England and 5% in the north-west, but a modest 0.8% rise recorded in London and 1.5% in the south-west and 2.8% in the south-east.
ONS head of housing Aimee North said: "House price annual inflation continues to pick up with the average UK house price now at around £269,000.
"Annual private rents inflation has slowed across the whole of the UK for the seventh consecutive month.”
Meanwhile, rises in rents eased.
Average UK monthly private rents increased 5.9% in July, down from the 6.7% annual rate in June.
Jonathan Hopper, CEO of Garrington Property Finders, commented: "After slowing sharply following the end of the Stamp Duty sugar rush, house price inflation is back with a bang."
However, he said the jump in the national rate "should be taken with a healthy pinch of salt", due to the wide variance across the UK, with "dizzying" growth seen in parts of northern England "a world away" from London's flatter rate.
He noted that London is back in growth territory, having been negative as recently as May, as sellers had to cut asking prices or agree to significant discounts in order to get their sale across the line.
"Price rises are modest in much of southern England too, and on the front line we’re seeing lots of high-value homes coming onto the market in sought-after areas.
"The surfeit of stock is putting buyers firmly in the driving seat and giving them the confidence and clout to negotiate hard on price."
With mortgage interest rates inching lower following the Bank of England’s decision to cut the base rate, Hopper said "buyer sentiment is strong".
A growing supply of homes to choose from means the dynamic between sellers and buyers is seeing buyers "engaging and deals are being struck", with families and upsizers re-entering the market, while demand for flats remains subdued.
"It reflects not only changing housing needs. but also the impact of borrowing costs on entry-level buyers and investors."