The registered keeper can indeed appeal, but there are stronger grounds than the ones you have raised. They are not seeking to make use of Schedule 4 of the Protection of Freedoms Act to hold you liable (and even if they were, they would probably be unable to by virtue of it not being 'relevant land' due to railway byelaws). The keeper could appeal along the lines of the below...
Dear Sirs,
I have received your Parking Charge Notice (Ref: ________) for vehicle registration mark ____ ___, in which you allege that the driver has incurred a parking charge. I note from your correspondence that you are not seeking to hold me liable as the registered keeper, under Schedule 4 of the Protection of Freedoms Act 2012 ("The Act"). As the land is railway land under statutory control, it is not relevant land for the purpose of the Act, and as such the charge cannot be recovered from me, the keeper.
There is no obligation for me to name the driver and I will not be doing so. I am therefore unable to help you further with this matter, and look forward to your confirmation that no further action will be taken against me. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
Appeal online if you can being careful not to identify the driver in any way. Keep an eye on your spam for their response and chase if you don't hear back.
- NCP fails to fully identify themselves on the letter
This point isn't particularly important due to the above, but I'm not sure what you mean by this. They state that they are National Car Parks Ltd, that they are the creditor, and also provide their company number and registered address. I'm not sure what further information you think they could or should provide to identify themselves here.