This is down from 36.9% three months ago and 40.4% one year ago which Zoopla said may indicate the housing market is starting to strengthen as homeowners feel less pressure to drop their asking prices.
However the average price reduction on those properties that have been discounted is up to its highest level in two years, now standing £20,612, compared to £18,993 three months ago.
The research also highlighted different parts of the country where either a larger proportion of sellers than average have been forced to reduce prices or the reductions have been greater than average often as a result of multiple price reductions.
The areas with the highest proportion of discounted properties included Wakefield (50.4%), Chesterfield (42.5%) and Barnsley (42.2%).
And the biggest percentage drops from original asking prices were in Romford (10.3%), Wakefield (8.9%) and Newcastle upon Tyne and Liverpool (both 8.8%).
At the other end of the scale, Edinburgh, Poole, Telford, Reading and Wolverhampton top the list of places with the smallest asking price discounts on offer currently.
Lawrence Hall of Zoopla.co.uk said: “The proportion of properties that have seen their price reduced and the average amount of the discount provides good insight into the strength of the local market. With the proportion of discounted properties nationally at a two-year low this would indicate that sellers are feeling more confident than they have for some time.
Hall added: “But there are places where the market clearly remains weak, such as Wakefield, where over half the properties on the market have been reduced in price at least once. Zoopla.co.uk has a unique feature that allows users to sort their search results by properties that have been most reduced in price useful for those buyers looking to snap up a bargain.”
