Home buyers are now paying nearly 97% of the asking price of a property, marking the highest average percentage seen in nearly 12 years, property analyst Hometrack has reported.
But there are early signs that the London market is starting to soften, amid evidence that buyers are becoming less willing to meet sellers' prices in the face of the recent strong hikes in house values seen in the capital, the report for April said.
Across England and Wales, prices rose by 0.6% month-on-month in April, which is the same increase seen in March - and the time it takes to sell a property has fallen to just over six weeks on average, marking the quickest time period for homes flying off the market seen since June 2007.
At 96.7% on average, the proportion of the asking price that house sellers are achieving has leapt to its highest level since September 2002, Hometrack said.
House prices lifted month-on-month by 0.8% in London and the South West, by 0.7% in the South East and East Anglia, by 0.5% in Wales and Yorkshire and Humberside, by 0.3% in the East Midlands, the West Midlands and the North West and by 0.2% in the North East.
Hometrack said that demand in the housing market is continuing to grow at a faster rate than the supply of homes coming on the market, which is keeping an upward pressure on house prices.
Outside London, 48% of postcodes registered higher prices in April, which is the most widespread coverage of house price rises for a decade. The greatest declines in the time it takes to sell a property over the last year have been seen in East Anglia where it is now just under five weeks, the South East where it is now just over four weeks and Wales, where it now takes around six weeks to sell.
But Hometrack also cautioned that London, which is seen as the engine of the housing market, is starting to see emerging signs of "price resistance" among buyers. The typical length of time it takes for a London property to sell has increased by almost a week over the last month to just under three and-a-half weeks. The proportion of the average asking price achieved in London has also edged down by 0.3 percentage points compared with a month ago to 99.0%.
Recent Office for National Statistics (ONS) figures showed that London house values have surged by 17.7% over the last year to reach £458,000 on average, while the UK as a whole has seen a 9.1% annual increase.
Richard Donnell, director of research at Hometrack, said of the London market: "While these changes indicate very strong market conditions, they suggest that buyers are starting to become less willing to bid up the cost of housing at recent rates."
Mr Donnell said that the impetus for house price growth looks set to spread across regional housing markets over the coming year.
But he continued: "What is less clear is the scale of pent-up demand that exists to sustain further house price increases.
"A continued improvement in the economic outlook and incomes growth is essential to sustain improved levels of market activity but the outlook for interest rates and the willingness and ability of households to take on mortgage debt are the factors that will influence the outlook over the medium term."
Toughened mortgage lending rules came into force on Saturday, which mean that lenders have to ask people looking to buy a home or re-mortgage more detailed questions about their personal spending habits to work out whether they can afford a home loan. They also have to apply "stress tests" to make sure a borrower could still afford their repayments as and when interest rates rise under the Mortgage Market review (MMR) rules.
Figures released last week by the British Bankers' Association (BBA) fuelled speculation about the possibility that the housing market could be starting to come "off the boil".
The BBA said 45,933 approvals worth £7.5 billion were given the go-ahead in March, marking the lowest number seen since last November, although this figure is still 43% higher than in March 2013.
The Government's flagship Help to Buy scheme has helped to boost the housing market by unleashing a stream of demand into the housing market over the last year from people with low deposits who may have previously struggled to get a mortgage.
But some housing market experts have pointed to recent surveys suggesting this demand may be starting to tail off. They say that combined with the toughened MMR lending rules making mortgage lenders more cautious, this could mean that the pace of the housing market recovery slackens.