Firstly, very sorry to hear about your father - I hope he's on the mend.
Secondly, so that you are going into this with your eyes open: there will be no quick or easy resolution to this matter, and PCM can be a litigious company. If you want to fight this, you'll need to be prepared for the possibility of defending this in court (a loss at court would probably be about £200-220, so this will depend somewhat on your attitude to risk).
In order to be able to offer detailed advice, we'll need to see a couple of things:
- A photo of the Notice you received from PCM (Show us both sides, redact personal information, leave on all dates and times
- Photos of the signage at the car park, showing their layout in the car park, any signage at the entrance, and also a close up so we can read the terms and conditions
- A copy of the appeal you submitted, and their response
Now to a couple of things from your post:
didn't have his blue badge present at the time [...]
PCM of course denied my appeal and stated that I need to have a permit to park there.
What was the charge issued for? If it was issued for not having a permit, then the presence or absence of a Blue Badge is irrelevant. A blue badge does not grant any special rights on private land, unless the signage in the car park explicitly says so.
It baffles me slightly that I am not allowed to park for a short while in a deserted car park to no one's inconvenience to drop off my brother.
By the looks of it, it is a residential car park, therefore there's a good chance residents of the adjoining building pay for use of the car park, with PCM hired to ensure the car park remains for their exclusive use as paying residents. The argument around it being empty won't fly - this is about whether a contract was entered into or not, and the car park being empty doesn't affect that (and at any rate, there's no way to know whether an empty car park will remain empty throughout one's stay).
(To note - I'll be away from tomorrow until Monday. If you don't get any replies before then, it's not because you have been forgotten about)