That's fine for you, but it doesn't change the point at all, which is that for most people, City is far from what they'd consider the centre. That Mayfair was on the outskirts a couple of hundred years ago is not particularly relevant. Startig in the late 18th century, Charing Cross[1] has increasingly been considered the centre, even occasionally being used as an official marker.

[1] https://en.wikipedia.org/wiki/Charing_Cross