Update to my original question.
In the private parking company's process. I have now passed the point where not knowing who the driver was, is an advantage to me, so I now know, however it is irrelevant.
I have investigated what has happened looked at the signs/street marking and found that the street parking company's signs and the permit they issued is not clear. As I said in an earlier post, there is an area controlled by the company. This covers two parallel streets, Street A and Street B. if you have a permit for Street A, it seems you can't park on Street B and vice versa. The permit the car was displaying gives no indication that it is for Street A only. The parking company's signs do not differentiate which area they cover, i.e. this is the sign for street A and this is the sign for street B.
Only Street A is marked by the council at one end, and there would be no reason for the driver to go to their home passing the sign, so would never see it. Street B is not marked in any way. One of the most important rules for parking companies is that the signs MUST be clear. In this case I genuinely believe they were not and the permit issued did not show for which street the permit was valid.
My plan is to continue following the company process and go to independent review, but if that fails, I will be happy to go to court. I firmly believe that a judge would agree the process was flawed and will reject the case. I would also request that all parking charges since the process was introduced should be reviewed to see which were issued incorrectly and should be repaid. Additional information is the driver was a nurse returning from duty in the evening, but she doesn't want that to be used. The PCN was issued at 6:02 in the evening. She genuinely thought she was parking in the correct place. The parking company has already rejected an appeal based on the driver thought they could park there.
I will inform the company of my intentions before going to independent review and give them a chance to cancel the charge (which is more than they gave the driver). I will have no fear going to court on this one and inform the company of my preferred course of action. I very much doubt the company would take the risk. If the company wins, I will pay the fine for the driver, If the driver wins, the company will have to go into a process of investigation and repay lots of fines/costs/ etc, so a big risk for them. There is no guarantee who would win. I believe it lies in favour of the driver, but it's really about who has the most to lose if they don't. I'm happy to take that risk.
I really believe in fairness. This charge in this particular instance is not fair. After this is done, in the name of fairness to other people who might have been issued with a charge under the same circumstances, I would contact the local council to make sure the company marking meet legal requirements and a street sign is put up. I would also request the parking company/council review ALL charges issued in that area to make sure they were issued correctly.
I have no problems with private parking rules but they are enforced by companies/people motivated by money and profits, so you must challenge them and ensure they are doing everything by the book and fair.