I'd argue that if your point around remote fully held true then that would be shown in the very short-term by rental prices (as the key indicator of people leaving London in lieu of population/census data) but that hasnt been apparent in the data. London rentals have seen much stronger growth post-covid than other places in the UK.

What is happening with house prices in london is a combination of the simple effects of high-ish interest rates v high house prices (limiting affordability) and also flats in general taking a beating from post-grenfell building regs changes and leasehold issues. When you look at granular data there is still a surprising amount growth in Zone 3-4 onwards in London because actual houses in those locations are still sort of achievable for decently paid couples.

Also regionally, a bit glib, but the price increases are happening in Manchester not Bolton or Sheffield not Scunthorpe. If remote working was truly acceptable then those latter locations would be seeing far more inward movement of people but they're not really