The proportion of homes selling for their asking price in England and Wales hit a 10-year high in March at 96.2%.
The percentage grew from 93.5% a year earlier, 95.3% in January and 95.8% in February, according to analysis from Hometrack.
In London, more than 99% of properties were selling at the full asking price in March. In East Midlands, the proportion was lower at 95.8. In East Anglia it was 95.7% and in Yorkshire & Humberside it was 95.5%.
Nationally, the average time it takes a property to sell has also fallen during the first three months of 2014. In January and February it took eight weeks, while the March figure of 7.9 weeks was the shortest average selling time since October 2007.
The reason for changes - and the fact that house prices moved up by 0.6% in March, compared to the previous month - is simple. Demand for housing continues to grow faster than supply.
Demand, or the number of new buyers registering with estate agents, grew by 6.6% in March, compared to February. Over the same period, supply - the number of properties listed for sale - fell to 1.9%, down from 11.2% in February.
Low rates and strong demand
Richard Donnell, director of research at Hometrack, said: "Much has been made of the impact of Help to Buy but the overall volumes of sales supported by the scheme remain relatively small. The real driver of higher house prices is record low mortgage rates and strong demand from first time buyers and investors who have no property to sell which is compounding scarcity.
"With average mortgage rates currently at 3% or lower, compared to over 5% before the downturn, households have seen a significant boost to buying power who are now being priced into the market on improved buyer confidence."
But while there has been an uptick in the property market, many prospective first-time buyers continue to struggle to raise a deposit and secure a mortgage.
Concern about saving a big enough deposit is at its highest for two years, according to the Building Societies Association.
According to a recent survey it conducted, 63% of people said it was the biggest barrier to buying their own home.