It's really not "essentially sovereign" or "outside national law" as you might argue of an embassy or a military base or even, say, the Channel Islands. People and businesses there are subject to all the laws of the land. Financial firms there are regulated by the FCA, which is based outside the City and appointed by the Treasury, definitely not by the City of London Corporation.
Prestigious financial firms have offices in the City because everyone else does, not because there's some legal or regulatory benefit from being incorporated there - again, very different from those who choose other Crown jurisdictions like Jersey or IOM or the Caymans.
This is definitely not true. Maybe you confused it with Isle of Man or Channel Islands, which are crown dependencies with certain autonomy, often accused to be British tax havens.
yes I am a wonk