Sales have climbed after dropping by 57 per cent in April, with August busier than usual years, analysis by the agency showed.
The stamp duty holiday and low interest rates are among the factors supporting house prices, despite economic uncertainty and a potential second wave of Covid-19, Knight Frank said.
The areas with more outdoor space and greenery will fare best, with the picture broadly flat across the UK.
Values across the UK are predicted to rise by two per cent overall in 2020 and by just one per cent in 2021.
In prime central London prices are set to fall by three per cent this year before bouncing back to four per cent growth next year.
The agency said it expects prime London to outperform the rest of the country over the course of the next five years, because values in this market have corrected by more than other markets over the past five years.