Legoman,
Just had a lengthy chat with my colleague.
They have advised that you ask for a full investigation into this case. Best practise would be to email them and copy in as may people as you can. i.e. corporate complaints, The Head of Service; who would be in charge of the car parks section. The Leader of the council, together with your local MP or councillor. This will not get ignored.
You also need to ask them why the charge is so much, as it sounds like its gone to a charge certificate level, you need to ask them what the initial charge was, and what the charges are as the case has progressed.
The onus is on the Council to prove that their system was followed to the letter. As i said it is NOT for you to prove you didn't receive the initial fine, as THEY are fining you.
Within the email or letter you need to provide all dates you were away, photos of the subsequent reminders etc, that you have received from them and attach to the email. I would also ask for a copy of the initial fine, together with the date it was sent out.(Not withstanding the postal strikes, that is irrelevant). If they have followed their procedures to the letter, which they have to, then they should be able to give you chapter and verse. Like I said as a Council they cannot call you a liar for non receipt of initial fine, the onus is on them.
Anyway good luck. Cheers.