You aren't familiar with reality, are you?
Yeah, I have no idea what I'm talking about. It's not like I've actually worked in London and the City of London and I'm not sitting in a hotel right now in the City of London (yes, I took that just now, just for you. You may recognise the famous Lloyd's Building in that picture on the left side), oh wait.
What does this even mean? There are villages that use the same roads as towns, that doesn't make them part of that town.
Actually, the service departments are separated from London? But even if it weren't, it's still considered a separate 'entity' in culture, history, legality and geography.
By your logic, taking out a piece of a completed puzzle, covering it in a colored marker, and then putting it back would make that piece of the puzzle separate from the rest of the entire puzzle around it
By your logic, it must be part of America because America is connected by the same planet.