This is a private land fine and they are members of the British parking association. The normal process is to send your appeal online or by email at day 25 of receiving the ticket. You can also put in a complaint to the landowner about the charges. This can sometimes work.
If rejected you’ll need to appeal to POPLA which is the independent appeals service. You should receive a POPLA verification code with their letter of rejection. The appeal to POPLA must be done within 28 days of receiving any rejection letter.
The important thing is not to be intimidated by any letters received and threats to send it to debt collectors. It is normal to receive these type of intimidating letters so expect them. Their function is to scare you into paying. You should be successful at the POPLA stage.
They have no legal basis to charge you the excess amount as they are merely invoices as opposed to fines. Normally with these private companies, they do have a claim for breach of contract but only to recover monies they have lost and not for excessive amounts.
If all your appeals are rejected, they may issue court proceedings, this is the only way for them to recover the funds. It is unlikely they will as it isn’t cost effective for them to do so, as cost of court proceedings is more than what they can recover but some companies do issue and if this is the case, then you’ll need to ensure you defend the matter.
Given the circumstances you are likely to be successful if they do issue and they would have wasted their time. These claims are defendable with a high success rate. Worse case (and unlikely) scenario is they win at court , and in that event you’ll just be ordered to pay the original charge plus court fees which is about £25. If paid within 28 days it doesn’t appear on your credit file. I would suggest just sending them a nominal sum like £5 or so to cover the charges , if this is accepted they’ll likely leave you alone. But if not, then the process is as above.
I hope this helps. Let me know if you have any further questions.