They are driven by the average income of the wealthiest $number_of_homes renters. If there are not enough homes in a single city then a lot of people will pay very significant part of their salary to have a place to live.
This is a very valid addition that I've skipped for clarity. But rental prices are very location-bound, and we can build only that much houses in a given location.
You can build up a lot, far more than is typical in much of London.
There are 3.6 million dwellings [0] in the 157,000 hectares of London [1]. There's 14,000 Hectares of Park and Open Space [2].
If you quadrupled the amount of park and open space to 56,000 hectares, leaving 100,000 for housing, and built as dense as Islington or Kensington+Chelsea (not particularly known for skyrise apartments), at 70 per hectare, that would be 7 million dwellings, about twice as many as now, even with far more public open space
157 000 hectares is a lot (pun intended). This is not one place, price of similar flat in the center and in the outskirt would be 2-3 times different just because of the location. You cannot consider those hypothetical dwellings similar.
They are driven by the average income of the wealthiest $number_of_homes renters. If there are not enough homes in a single city then a lot of people will pay very significant part of their salary to have a place to live.