House prices fell by 0.1% last month according to the Halifax house price index, following a 1% increase in March.
The average house price now stands at £168,202, 6.6% higher than the same time last year but 16% below the peak of August 2007.
Halifax says that the improvement in house prices since April 2009 has encouraged more sellers to come to the market.
Martin Ellis, housing economist at Halifax, says: “The underlying rate of house price growth has slowed in recent months following the relatively sharp rebound, albeit from a low base, in the second half of 2009.
“New sales instructions have risen, helping to push up the stock of unsold properties in recent months.
“As a result, the imbalance between supply and demand is easing somewhat.
“Our view is that house prices will be flat during 2010 as a whole.”