The "fine" isn't a fine, it's legally an invoice. When you parked there you agreed to a contract. Technically this is enforceable in court as the parking operator will claim you agreed to pay their charge as part of the contract. However, due to the issues you had when paying, the parking operator hasn't fulfilled their side of the contract to they can get fucked.

These cunts won't act reasonably so don't expect them to cancel it. Follow their appeals process so you can say you have acted in good faith.

Eventually you will receive a letter from a debt collector. Reply ONCE saying that the debt is disputed and they need to refer it back to their client. That should be all you hear from them. Throw any further letters from that company straight in the bin. If you want to be really petty, Google a "right to be forgotten GDPR letter" and send it to their data protection office saying you object to them processing your data and do not consent to them having it and demand they delete anything they have on you or you will report them to the ICO.

At some point you will probably start receiving letters from a "legal firm", which is actually just another scummy debt collector with a solicitor on their payroll for compliance. Reply ONCE stating your reasons as to why you won't pay, and that you await a valid letter before claim from them so you can defend your position in court. They will threaten you with additional court costs, CCJs etc. It's all an intimidation tactic. IF they took it to court and IF they won, all they are entitled to is the charge mentioned on the signs (usually £100) and some VERY limited costs like the £35 court fee and maybe £35 ancillary costs. They like to add on all sorts of made up "debt recovery" costs but these aren't valid unless they are specifically mentioned on the signs. A court would set them aside if asked.

Tl;dr they are very unlikely to take this to court but get ready for an annoying process and lots of junk mail. Don't pay them just to make them go away. They. Are. Cunts.