Big cities are big enough that you can have vastly different ideas of what it means to "live in New York" or "live in LA" - I had friends in both who would say they lived there, but were a minimum an hour from the central business district.

Yeah. You get people who live in Bromley who say they live in London, just because it's a London Borough.

I gave up answering where I lived years ago, now I just reply with the name of the nearest international airport; people are much more likely to know where LA is than any of the hundreds of smaller cities in and around its metro area.

As somebody who lives well outside London, my mental model of "in London" is "within the M25" :-)

Real Londoners use this.