The latest UK Cities House Price Index shows the capital’s annual growth rate climbed from 2.3 per cent in June to 2.8 per cent in July.
Prices in the capital have consistently risen at an average of 0.5 per cent for the last six months and are now 1.4 per cent higher over the last three months.
Hometrack said the stabilisation was due to lower transaction volumes and an absence of forced sellers.
Housing turnover across London has fallen by 17 per cent since 2015 as affordability pressures and recent policy changes impact demand, leading to a low rate of nominal house price growth that is expected to continue until at least the end of the year.
Richard Donnell, research and insight director at Hometrack, said: “The downward pressure on prices is greatest in the most expensive parts of the capital where demand has been weaker since the end of 2014.
“These inner London markets are registering small year on year price falls of up to 2 per cent. The downward pricing pressure is less evident in the lowest value markets of London which have registered above average growth and price inflation of over 3 per cent.”
Annual house price growth across UK cities fell from 7.4 per cent in June to 5.3 per cent in July.
Birmingham (8 per cent), Manchester (7.1 per cent) and Nottingham (6.9 per cent) continued the trend for strong growth in regional cities.
Aberdeen remained the only UK city in the top 20 list to suffer house price falls (-3 per cent), and average prices in the city are now 16 per cent lower than they were in December 2014 due to the fall in the price of oil.
Jane King, mortgage adviser at London-based Ash-Ridge, said she had been witnessing small price increases, mainly due to a lack of supply.
“It is area-by-area,” she continued. “Some parts of west London, such as Chiswick and Hammersmith have been going up, whereas perhaps not quite so much in other areas.
“They are starting to rise again, but I think a bit of it is due to a shortage of supply. There is even a lack of shared ownership available.”
Ms King added that a recent rise in equity release levels could be down to more parents helping their children to get on the housing ladder, and that may be putting upward pressure on prices.