The property portal said this was a monthly rise of 0.8%, equivalent to £2,807.
The rise has come from pent-up demand for property being released during the traditional spring selling season.
It added that asking prices are up by 0.6% in the last 12 months.
The number of sales being agreed during the first four months of the year is 17% higher than last year, outstripping the 12% increase in the number of new sellers coming to market.
Tim Bannister, Rightmove’s director of property science, said: “Some predicted that property prices would suffer sharp falls and take a while to recover following the Bank of England increasing the base rate up to 5.25%, where it has remained since August 2023.
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“However, the momentum of the spring selling season has exerted enough upwards price pressure to reach a new record asking price.”
Take action now to move by Christmas
But it’s not all positive news for the property market.
Despite positive indicators for higher transaction levels this year, it takes an average of 154 days between agreeing a sale and legal completion, which Rightmove described as “a challenge for both agents and movers”.
It added that, with 62 days on average needed to find a buyer before the legal process even begins, “would-be sellers hoping to be in a new home for Christmas need to be taking action now”.
In total, it now takes over seven months on average from a seller coming to market to completing their move.
Bannister added: “The extremely lengthy legal completion process is a frustrating barrier to homemovers converting agreed sales into completed transactions more quickly.
“It may seem surreal to be thinking about Christmas in May, but we know that many would-be sellers picture celebrating the festivities in a new home, and to achieve that, now is the time to be coming to market.
“One strategy that is still giving some sellers the edge in this price-sensitive market is working closely with an estate agent to price attractively right at the start of marketing, to give themselves the best chance of finding a buyer quickly.”