The uptick follows the reopening of England’s housing market following the coronavirus lockdown.
Rightmove director Miles Shipside said: “The unexpected mini-boom continues to gather momentum.”
Mr Sunak announced the stamp duty holiday with immediate effect on 8 July as part of a package of measures designed to boost the beleaguered economy.
It means that until 31 March next year the threshold for paying the property transaction tax has been lifted from £125,000 to £500,000.
The Rightmove data showed asking prices between June 7 and July 11 climbed by 3.7% to hit a record high average of £312,625. That was 2.4% higher than before the lockdown began in March.
Mr Shipside said: “The busy until interrupted spring market has now picked up where it left off and has been accelerated by both time-limited stamp duty holidays and by home owners reappraising their homes and lifestyles because of the lockdown.
“These figures are the earliest indicator of house price trends
“They show on average prices gently rising not falling, and this will be reflected in the coming months in other house price reports.”
There are also signs that banks and building societies are tightening the availability of home loans.
But the Rightmove figures pointed to a sharp recovery in interest from potential buyers.
They showed that buyer enquiries across Britain as a whole since the start of July jumped by an annual 75%.
Last week, Bank of England Governor Andrew Bailey said there were signs of activity returning “quite strongly” in the housing market.