It’s not clear at all that the vast majority of people in London commute by public transport. The sources linked below, one during the pandemic in 2020, and the other a series of estimates, suggest the figure is more like 25-35% but I wasn’t able to find something more conclusive. [1, 2]

More to your point, I agree that SF or at least the Bay Area has a higher dependence on cars, but it’s also more geographically constrained by the bay and resulting bridges/ferries, so it’s not obvious that there’s much more freedom in where to live in practice. For instance, I would guess a one hour commute in London would encompass a similar or greater number of housing units than in the Bay Area.

Somewhat unrelated, but London seems relatively low in public transport usage compared to virtually every large continental European city [3], which at least anecdotally tend to have much cheaper transport (particularly for monthly/annual subscriptions for commuters) and/or somewhat less car-friendly infrastructure. Riding a bus through Old Street, for instance, makes apparent one cost Londoners pay for not prioritising public transport.

[1] https://www.london.gov.uk/who-we-are/what-london-assembly-do...

[2] https://www.london.gov.uk/who-we-are/what-london-assembly-do...

[3] https://www.researchgate.net/figure/Modal-shares-in-selected...