But renters on Wednesday night issued their own warning that “lots of expensive market-rate housing won’t bring housing costs down to affordable levels for the millions of people trapped in poverty by sky-high rents”.

Sure it will. Housing price is a function of supply and demand, like everything else. If you don't have enough supply of housing in London for people who want to live in London, then what happens is that housing prices rise until sufficient people are priced out.

If a developer builds new housing, then someone is going to live in it. If that person is living in that housing, then they aren't living in some other housing in London, which will make that housing more-affordable.

But what if a developer only builds luxury housing and nobody wants to live in it?

A developer has a pretty strong incentive not to build something that nobody actually wants, so that's unlikely to be a serious problem -- their incentive is not to do this. But, sure, assume that happens. Then that developer is going to need to recoup what they can by selling the development for what they can, even at a loss. The parties who invested in that development will wind up covering some of the cost of buying housing for people in London.

What's at issue isn't "fancy housing" or "not-fancy housing". It's the quantity of housing. Build more of whatever type of housing, and the price of housing will drop.

As long as one can profitably build housing -- the price of land and the price of construction and a reasonable return is lower than the price of housing -- developers have every incentive to build. They only won't build if they aren't allowed to do so.

Removing or relaxing London's height restrictions might be a good place to start.

https://archive.ph/jRQIm

https://en.wikipedia.org/wiki/YIMBY_movement