The appeal is quoted above in IMG_5586
There may be a similar POPLA appeal here on the forum, there is a search capability, from everything said here the “parking company” has no contract indeed, your right to use the parking space trumps them.
If POPLA doesn’t uphold your appeal, the speculative invoice would not stand up to court scrutiny. It would definitely help to know exactly which useless money-grabbing bunch is trying it on here.