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.......