The average asking price of a house has reached a record high for the fourth consecutive month.
Rightmove said that the average price tag on a property this month is £367,501 - up from £360,101 in April.
In the past two years, the price has soared by £55,551 - compared with the £6,218 increase seen in the two years before the coronavirus pandemic.
Rightmove said that over 20 years of tracking property prices it had never before seen such frenzied market activity.
Tim Bannister, Rightmove's director of property science said: "What the data is showing us right now is that those who have the ability to do so are prioritising their home and moving, and the imbalance between supply and demand is supporting rising prices.
"Though demand is softening from the heady levels we saw this time last year, the number of buyers inquiring is still significantly higher than during the last 'normal' market of 2019, while the number of homes for them to choose from remains more constrained.
"We anticipate that the effects of the increased cost of living and rising interest rates will filter through to the market later in the year, and a combination of more supply of homes and people weighing up what they can afford will help to moderate the market."
The figures also show:
• The number of properties for sale is 55% lower than in 2019
• The number of buyers contacting estate agents is 14% down on the stamp-duty-fuelled market of this time last year but still up 31% compared with the pre-pandemic market of 2019
• The number of sales agrees is up 12% in the year to date compared to 2019, but it is down 17% compared with the same period last year
John O'Malley, chief executive at estate agent Pacitti Jones in Glasgow said: "Whilst frenzied buyer activity has calmed down, the market is definitely holding strong and we are now seeing higher volumes of vendors feeling more comfortable about putting their property on the market before making an offer on another.
"Pricing remains very robust with substantial offers being made across the whole market."
Aled Ellis, director at Aled Ellis & Co in Aberystwyth, said: "The property market is still buoyant in our area despite inflationary pressures and higher interest rates.
"The trend is set to continue as there is very little coming on the market, and when it does we agree a sale very quickly.
"Since COVID, we're still seeing a lot more people are able to work from home, and wish to live in rural areas as long as the broadband connection enables them to do so."