It's my understanding that the Corporation administers local government in the City, and it is itself plutocratic rather than democratic, but otherwise Parliament's laws for England apply just as well within the City as without. Banking regulations and so forth that govern business in the City come from FCA, which came into existence by an act of the UK Parliament.

I mean, Manchester has its own police force, Merseyside has its own police, and so forth. Each borough in the England has its own elections. What's peculiar about the City is that the electorate of the City's elections includes businesses as well as residents. But it's not some kind of extraterritorial oddity as some conspiracy theorists think.