The average price tag on a home reached a record high of £308,075 on average in May, a property website has reported.
Across Britain, the price of fresh properties coming to market jumped by £2,343 or 0.8% month-on-month.
But different markets are still operating at different speeds, and the overall picture is one of a less buoyant market, both in terms of price growth and number of sales agreed, Rightmove said.
It said record visits to the website indicate a continued strong interest in property, but uncertainty and stretched affordability have led to more hesitant buyers and sellers in some areas.
Miles Shipside, Rightmove director, said: "After six years of continual year-on-year price growth the current market is becoming increasingly price-sensitive, with new-to-the-market sellers being limited to an average asking price growth of just 1.1% over the last year.
"This is in spite of there being plenty of historically cheap mortgage products around for buyers who meet lenders' criteria.
"Sellers need to pitch their price at a tempting level to entice buyers, as while there are signs of strong demand there appears to be hesitation among some buyers to commit."
Rightmove said a lack of homes for sale means estate agents in some areas report that the right property at the right price is still selling briskly.
It said annual rates of asking price growth of over 4% are still to be found in the East Midlands (4.8%), the West Midlands (4.3%) and Wales (4.3%).
London and the South East are the only regions where asking prices are lower year-on-year, down 0.2% and 0.1% respectively.
In Scotland, asking prices are up by 2% annually.
In the North West and Yorkshire and the Humber, asking prices have increased by 3.9% annually, while in the North East they have grown by 0.4% and in the South West they are up by 2.9%. In the East of England asking prices have increased by 1.7% year-on-year.
Mr Shipside continued: "The last time the South East recorded an annual price fall was in 2011, indicating that the softening in the London market is now spreading to its commuter belt, while there are signs that inner London may be closer to a price recovery.
"While this gives buyers in the South East the opportunity to negotiate prices down, in some of the more buoyant areas of the country the options to do so are more limited by a shortage of suitable properties on the market."
Rightmove also quoted Liz Brown, divisional managing director at estate agent Connells, who said: "London may have lost some ground for now, so it seems the Midlands is where the next smart money is going."
Meanwhile, Russell Quirk, founder of Emoov.co.uk, said: "Over-optimism on the side of UK home sellers is continuing to push asking prices ever higher."
He said this "is becoming a big problem and the widening gap between asking price and sold price will only result in a further decline in buyer interest and a continued market slowdown".