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No room? You'll have to knock buildings.
I think people get into the habit of thinking about London and seeing just narrow roads like the ones off Seven Dials or their own residential roads. London, as everyone knows, is a big place and there's a lot of big, arterial roads where there is plenty of space for segregated lanes. There's no need to scratch putting in lanes on these just because other roads are narrow. The upshot is that you'll probably get a lot of unlinked cycle routes but at least then you'll have something to link up. Also the changes that the sections bring about could make it easier to design those links, they certainly won't make them worse.
No room? You'll have to knock buildings.
Forget segregated lanes, spend money on improving the road surface, also we've got plenty of bridges to cross, leave the garden bridge alone ;)
I like the focus on better provisions for bike locking though.