Who are 'they'? There is no official thing called a 'knife ban', and again, there are no laws about knives specific to London. There aren't really any laws about anything that are specific to London, as there is no corresponding legislative body.

Swords aren't considered knives, they are considered (correctly) to be bladed, and thus to fall under the scope of various bits of legislation, like this: https://www.legislation.gov.uk/ukpga/2019/17/section/41