The City of London isn't legally reliant on a charter. It draws existence from 'Time Immemorial'.

Specifically it exists because it existed before 1189

This is a good and subtle point of law -- The City of London is a corporation "by prescription".

But while it was created by neither statue nor royal charter, I doubt the parliament could not end it if it so decided....

That's why the City has the Remembrancer https://en.wikipedia.org/wiki/City_Remembrancer taking care of the City's business in the Parliament.

The King-in-Parliament can abrogate common law.