Investing in cycling infrastructure is a magic bullet to help advance three key policy areas for any society. Public health, overcrowded public transport / congested roads and CO2 reduction.
However, it's really your last point I was thinking of. It's a haphazard city of narrow streets given over to cars. That makes it a hard problem to solve.
As I said, anything is possible with enough will.
My borough of Waltham Forest, at least the parts inside the north circular, has segregated cycle lanes pretty much everywhere. Nextdoor in Haringey, not so much.
It's chaos for just about everything else too, especially when it come to IT. Every council outsources the exact same functions to different companies and almost none of them do it well. It's a collosal waste of resources.
Just as that other Roman town Lutetia. Paris and London are very similar in a lot of respects.
https://en.wikipedia.org/wiki/Haussmann%27s_renovation_of_Pa...