Parking Eye issued a "fine"

[jamesgmg]

Legally you don't have to pay parking fines if they aren't from the council or the police

Perhaps so, but it won't stop Parking Eye trying to take you through the small claims courts. They have won cases here and they have lost plenty too (well documented over at pepipoo), depends on the circuit judge on the day, their interpretation of contract law and probably what mood they are in.