I live in central London and pay a lot of rent, but I disagree, I don't think it's possible to compare London rents to New York. Certainly, the average rent across the entirety of London might average out at similar levels because there's a large number of renters and the floor is higher but at the upper levels, our rent is cheaper: you can live in almost any building in London for £3k/month, it's almost impossible to find an apartment building here where the rental floor is >£3k/month, luxury in London is comparatively cheap.
Not that I want to get into an argument on this (both cities are fantastically expensive), but the first property on your link when I accessed it (so basically at random) - GBP 5590.00 pcm.