Prices for homes worth more than £1m have continued to rise at a surprising rate this summer as cash-rich buyers chase limited supply, according to data from two leading estate agents, to be published on Friday.

Prime house prices in central London rose by 1.3 per cent in the past four weeks, their sixth consecutive monthly rise, according to Knight Frank. This meant the annual rate of change improved to minus 8.9 per cent from minus 12 per cent in August.

Savills said prime London prices rose by 4 per cent between June and September this year, following a similar rise in the second quarter. Price growth in some areas exceeded 9 per cent since March this year, notably in affluent London areas such as Chelsea, Kensington and Notting Hill. Average prices are still 18 per cent below their March 2008 peak, however.

Liam Bailey, head of research at Knight Frank, said: “The rude health of the central London housing market continues to surprise.”

The key drivers were tight supply, low interest rates and strong overseas demand from cash buyers, he said.

Savills estimated that only a quarter of prime purchases involved borrowing this year.

Knight Frank said that the volume of property on the market in September was down nearly 30 per cent year-on-year and was almost half the level of September 2007. According to Savills, stock levels are 20 to 30 per cent lower than the medium-term average.

Even so, Knight Frank’s London sales in the first three weeks of September were 75 per cent higher than in the same period last year.

Demand remained strong, with viewing levels up 80 per cent and the volume of prospective buyers up 30 per cent.

The family-orientated markets of south-west London also saw strong rises comparable to those seen at the height of the market in 2007, according to Savills. In the three months to September, prime property prices in the belt running from Fulham to Richmond, including Clapham and Wandsworth, rose by an average of 8.4 per cent.

Mr Bailey said price rises looked sustainable in the short term because of tight supply, but the real test would come when interest rates rose.