Depends if the rate of take up of cycling increases IMO. The year on year increases have been pretty consistent and don't seem to be slowing down. Sadiq putting on 'hold' (read cancelled) any new cycling infrastructure is likely to put an end to that though.
Don't forget we've got Crossrail coming later this year as well. That should take some strain off the central line in the mornings at least. Quicker Crossrail 2 get's off the ground the better though as the Northern line is a living hell in the morning. Getting on at Clapham (anywhere) and going north just is a 5 to 15 minute wait.
The soil beneath London isn't a infinite resource either, Crossrail 1 was threaded in between other underground services, with a margin of about 30cm in one case I believe.
Mayors seem to have pet transport projects, Ken had buses, Boris had bikes, What's Sadiq's?
Worryingly he doesn't have one.
An alternative solution worth investigating would be to ease rush-hour by incentivising, or even restricting, companies from starting at 9am.
I've been at startup-like tech companies in Shoreditch where it's acceptable to swan into work any time before 11. Another anecdata is the large bank I worked at where it was expected that you would work from home 1-2 days per week.
Brits are somewhat opposed to "tower blocks" because they were a poorly-planned top-down social engineering experiment in the postwar years to deal with rehousing the residents of slums and other deprived areas. Modern "high-end living" flats in much taller, aesthetically pleasing, and most importantly: safer, structures are being built, but not at a sufficient pace.
A reasons there hasn't been a total crash yet is because lovely, lower-density houses (think: 3 and 4 story spacious townhouses, not working-class 2-up/2-down terrace houses) are bought up for millions then internally gutted and remodelled into individual, modestly-sized flats to rent - sometimes barely larger than the size of a living room.