The first appeal is key to what happens later, and whether it is likely to progress to a claim (if the parking company is aggressive) or whether your parking charge ends up in the 'too difficult' pile. Before you draft your appeal, have a look at the range of defences here to see which are appropriate to the facts of your case. Mitigation/excuses are never accepted but if you have protected characteristics under the Equality Act and they are relevant to the issue, then advise the parking company early.
The next decision is whether the appeal should mention who was driving or whether to leave it to the parking company to prove. There are advantages either way, so go with what you feel is right for your case
Lastly, there are internet templates such as here which are useful to show how the appeal should be presented BUT they must be adjusted to your facts / evidence and should never contain anything that cannot be proven after a bit of research
If the parking company rejects your appeal, you have a second chance to appeal at the Alternative Dispute Resolution (ADR) stage. The ADR result is binding on the parking company but not on the person that appeals. Generally with companies that are members of the British Parking Association, it pays to make the second appeal to POPLA (Parking on Private Land Appeals). You can use the same first appeal or a completely different one, for example if more facts have come to light. Some parking companies will fold at this stage to save the charge they have to pay for POPLA.
The simplest and best way to get these charges cancelled is to complain to whoever hired the parking company. Typically they will have been hired by the site management - Managing Agents for Retail Parks; Residents Association/Housing Association for residential parking; Estates Department at Hospitals; or the Office Managers for commercial properties. You may have to try two or three times to get them to listen but they can get it cancelled if you press them.