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Class A shithousery!
Indeed, right from the start. A hire company (or any registered keeper) is supposed to tell the competent authority who they believe was driving the vehicle at the time, so that the authority can reissue the PCN to the driver. If they had done that, you could have appealed directly to Camden and you'd only be out the admin fee. I've had plenty of success with multiple boroughs appealing incorrectly issued PCNs.
IANAL so you need to ask somebody who is whether Zip are even allowed to pay off PCNs without first letting the authority pursue the driver, and whether their policy of doing so even if legal amounts to an Unfair Term
Class A shithousery!