The population of the City of London is under 5000 people.
And Jared is right it is only the area around Swiss Re, Tower 42 and the Lloyds Building.
They used to all be separate cities until about 200 years ago when they all grew together and the GLA (Greater London Authority) decided they should just be called bourghs of one large city.
See the tiny City area in the middle
You could split it up but it would result in 20+ extra places being made and people would wonder why they can't find the Canary Wharf buildings, Houses of Parliament, London Eye, BT Tower, London Bridge Tower, Tower of London, Tower Bridge etc. (most of the famous buildings) when they search for the London diagram.
This is what a City of London diagram would look like.