It sounds confusing but "London" and "the City of London" are not the same thing. The City of London is London's financial district. Why a corporation? I should think that's rather like a municipal council and works to control the various shenanigans that go on in the City.
The City of London "the square mile" which is also its own county, with flag and coat of arms is a Corporation. It has responsibilities beyond its borders financially and legally.A corporation is a company or group of people authorized to act as a single entity (legally a person) and recognized as such in law.