Rightmove said on Monday its asking prices for residential properties rose by 1.7% in the four weeks to April 13 when compared with the same period last year.
Prices sought by sellers rose by 1.1% in month-on-month terms, slowing from a 1.5% increase in the previous four weeks.
The average new seller asking prices of 372,324 pounds ($463,320) was only 570 pounds of a record hit in May 2023, Rightmove said.
Other measures of Britain's housing market have also shown a recovery in demand and prices, helped by a fall in borrowing costs which surged in 2022 when former Prime Minister Liz Truss's plans for sweeping tax cuts upset financial markets.
Rightmove said the number of new sellers was 12% higher than a year earlier and the number of sales was up by 13%. Demand was strongest in the high-end segment where asking prices in 2024 so far are up by the most since 2014.
Demand for properties typically sought by first- and second-time buyers - who are typically more mortgage-dependent, rose by less, the survey showed.
"Despite the current optimism, these are not the conditions to support substantial price growth," Tim Bannister, Rightmove's director of property science, said.
"Sellers who are keen to secure their sale will still need to price realistically for their local market and avoid being over-ambitious."