Also, very likely, it is largely a "replacement market", i.e. people that already own a flat or house in London decide to sell and buy a (larger) house in the country or in a nearby town, so there should be a flood of houses for sale in the city.

I mean I doubt that most people can afford to buy another house, keeping the one in London, or that most people that are now in a rented house can afford to buy one (even if outside the city) "suddenly".