The average price tag on a home reached a record high in May after jumping by £6,647 or 1.8% month-on-month, according to a property website.
Across Britain, the average asking price for a home coming to market is £372,894, Rightmove said.
The 1.8% month-on-month increase in the average asking price is the biggest of the year so far, it added.
However, the current “hyper-local” market is still price-sensitive and buyer affordability remains stretched, Rightmove said.
Tim Bannister, Rightmove’s director of property science, said: “This month’s strong jump in new seller asking prices looks like a belated reaction and a sign of increasing confidence from sellers, as we’d usually see such a big monthly increase earlier in the spring season.
“What is much more likely is that the market will continue to transition to a more normal activity level this year following the exceptional activity of the pandemic years.
“Steadying mortgage rates and a generally more positive outlook for the economy are also contributing to more seller confidence, though there are likely to be more twists and turns to come.
“The market is still very price sensitive and it is important that new sellers do not damage their prospects of a sale by overpricing initially and reducing later, with agents reporting that it’s the realistically priced new instructions that are selling best.”
The average discount from the final asking price to the agreed sale price has steadied at an average of 3.1%, in line with pre-pandemic market levels, Rightmove said.
The number of buyers making inquiries to estate agents about homes for sale is now 3% higher than at this time in 2019, led by buyers taking their first or second step on the property ladder, it added.
However, there are signs of some over-optimism in the “top of the ladder” property sector, Rightmove said.
While larger properties are still selling faster typically than in 2019, it is now taking an average of 67 days to agree a sale, nearly double the 35-day average at this time last year, the website added.
Mr Bannister added: “This month’s record price is a strong indication of sellers’ confidence, and we can see from activity levels and the still relatively limited choice of property for sale that this confidence is justified in some segments of the market.
“More discretionary sellers at the top end may be prepared to price high and wait for the right buyer, and whilst it is positive that they appear to feel no financial pressure to sell, the data suggests that some sellers in this sector will need to price more competitively if they want to find a buyer in the current market.”