Yeah the way this goes is before the monarch enters the city of London, the Lord Mayor of London presents them with a sword as an act of swearing fealty. This ritual has been turned by urban myth into the monarch having to ask permission to enter (which is not true- they don't have to ask permission and they don't ask permission). The crown also doesn't own most of the UK or even London. The monarch is the Duke of Lancaster[1] so if you die without a will in some areas of the North the crown can actually get all your stuff and they own a bunch of castles and estates etc. The Duke of Westminster is one of the UK's richest people as he really does own most of the real estate in Mayfair and Westminster so everyone in a building owned by "Grosvenor Estates" is paying rent to that dude.[2]
What is true is if you go to London you can see the boundaries of the city of London which are a set of cast iron dragon markers you see around and about on all streets marking the ancient boundary between Westminster and London.[3]
[1] Weirdly this was true even when Queen Elizabeth was the monarch. She was the Duke of Lancaster, not the Duchess. Apparently a female spouse of a Duke is a Duchess but if it's you and you're female then you're the Duke. I don't make the rules. https://www.duchyoflancaster.co.uk/
[2] https://en.wikipedia.org/wiki/Hugh_Grosvenor,_7th_Duke_of_We...