Pay up? Are you mad? they are crooks and nothing more. You need to read a few thread about them and also try and understand the law that surrounds parivate parking.
OK the signage is short and sweet, but isnt an offer of a contract.
The sign that refers to other non-existent terms has the wrong BPA logo on it and the one saying you pay £100 for breaching the terms doesnt indicate who the ATA is at all so neither fulfil the needs of the POFA and that should mean the DVLA have to refuse them access to the database but unforunately the DVLA doesn check anything and allows them free rein. An argument for later but at the moment you get on to KFC headquarters and popint out that CEL are abusing their position and that you hold the liable and will name them as co-respondents when you sue CEL for breach of the GDPR.
so get on to KFC pronto (forget local manager), you need the bosses to get on to their landlord with some reason to help you and being sued by you should focus their attention. Ignore CEL as the wording fo their NTK wont be POFA compliant but bear in mind they only make money by dishonesty and bullying so you must expect a long battle over this but you will ultimately win.