Prime central London prices have now fallen 23.6% since their March 2008 peak.
Knight Frank said that this month’s recovery was led by Chelsea, Kensington and Mayfair – where prices rose by more 1%.
In terms of price bands, the sub £1million bracket saw the biggest improvement, with a rise of 1.6% in the month.
The weakest price band performance was the top end (£10million-plus) segment which saw another weak month with a 2.2% fall.
Liam Bailey, head of residential research, Knight Frank, said: "It might be an old chestnut but it unfortunately remains true – don’t read too much into one month’s figures.
"Nevertheless house price growth of 0.4% in central London’s exclusive postcodes reflects a growing trend towards stronger market conditions which has been developing since the turn of the year.
"Since January, viewing levels and applicant volumes have been steadily rising – and in April were up by 45% and 32% year-on-year. Allied to these positive figures was a decline in the rate of price falls from the Q4 monthly average of around 3% to 1.5% and 1.6% in February and March respectively.
"The tentative recovery in prices has been led by the lower price bands (sub-£1million), rather than the more expensive price bands – in fact prices for the most expensive properties, the super-prime £10milllion + bracket, fell again in April by 2.2%. The better performance at the lower end of the market reflects (a) the fact that investors have been a significant driver of demand in recent months and (b) that this end of the market was hit earlier and harder by price falls in 2008.
"Our view is that price falls are almost at an end for the central London market – however we should not be surprised to see some negative monthly results through the year. The most significant issue remains sales volumes – which have risen over the past three months on a year-on-year basis by 28% – but which are likely to be constrained by a lack of stock over the next three to six months."
James Pace, head of Knight Frank Chelsea, said: "Recently we have seen a change of attitude in buyers with them losing the fear factor about prices falling considerably further and this has resulted in us agreeing more sales in the last six weeks than in the previous six months.
"The weakness of the pound has meant that buyers, most notably based in euros or dollars, have come to the market looking to take advantage of the favourable conditions that now exist. We are also seeing some buyers taking the opportunity to upgrade. As a result, sensibly priced property is receiving multiple bids and stock levels are reducing and we foresee this trend continuing into the early summer."
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