Atinas - your "pink bits". The big one is EGR 160 inside which any helicopter having an engine failure must be able to either glide clear or be able to ditch in the river. There is no law saying that you HAVE to ditch in the river.
The smaller ones were put in post-9/11 and have a ceiling of 1400ft. They "protect" Westminster, Buckingham Palace, The City and the Canary Wharf business district.
Whilst on the routes you are exempted from the 1000ft rule, but 500ft still applies. (Which has caught out a few near the Eye.) And The Shard now produces a "shadow" that still has an effect on the north bank - Shard is 1250ft so the theory is that off-route within 600m of it, you need to be at 2250ft. You won't always be offered such a clearance by City ATC.......