The research firm also reports a widespread lack of supply throughout London and the south-east.
Knight Frank reports a similar picture for prime London house prices, which it says rose 1.3% in September.
It is the sixth consecutive monthly growth, although prices are still 8.9% lower than 12 months ago.
Liam Bailey, head of research, said London prices are rebounding because of tight supply, low interest rates and strong overseas demand.
