To add a little colour to this. The resident population of the city is less than 10k - I’d guess around 3-4k in one development the Barbican Centre - but 500k work there. 10k is about one tenth of the population per Member of Parliament in the U.K.
The City of London Police number just over 800.
So the demographics for a ‘city’ are very odd too.
I went on an architectural tour of the Barbican Centre a few years ago - it was great, highly recommended (particularly if you're a fan of Brutalism, an under-appreciated style). Anyway, the (excellent) tour guide explained the reason that the development has the 3-4k population mentioned above. Apparently the destruction of housing stock caused by WWII bombing of the City was such that the population no longer justified the appointment of an MP. The Corporation of London weren't willing to lose their representation, and so immediately decided to rebuild precisely enough accommodation to be entitled to an MP - hence the entire Barbican development.
I've no idea whether that's true, but it fits in with the general opaque feudality that is the City.
Also: if faced with a zombie apocalypse, the Barbican would be a very good place to hold out. Good sight lines, few street-level entrances, a surprisingly large network of tunnels and the largest greenhouse outside of Kew... perfect!
I am afraid that story is codswallop. The City of London lost its 'own' seat in the House of Commons before the decision to develop the Barbican as residential was made. (Since the 1950 election the City of London has been part of the Cities of the Cities of London and Westminster parliamentary constituency.)
The City of London Police number just over 800.
So the demographics for a ‘city’ are very odd too.