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No, permeability is crucial for cycling. As I said somewhere up there, if you send cyclists on diversions or force them to walk, you reduce cycling. Pedestrian zones are one of the main reasons why cycling went down in post-war decades. Interestingly, as I've been expecting for a while, something similar now seems to have started/be going on in Amsterdam:
You don't want cyclists to have to use 'alternatives'. You want them to be a visible presence on hugely important streets like Oxford Street.
I don't really see the big issue for cycling, there are plenty of parallel roads you can use as alternatives. If it gets rid of the bus / cabs hellscape that is there currently and makes it pedestrian only I am all for it. London needs nicer public areas, it was so clear during lockdown how car traffic cuts up the city and makes large parts inaccessible.