First thing to do is edit your post on here. Do not reveal who was driving. "The driver" parked and you'll deal with this as the keeper.
blue badge clearly displayed
Unless stated on the signage, a blue badge affords no additional privileges on private land.
However, as this is a Horizon charge, send an appeal along the lines of the below:
Dear Sirs,
I have just received your Parking Charge Notice to Keeper _____ for vehicle VRM _____
You have failed to comply with the requirements of Schedule 4 of The Protection Of Freedoms Act 2012 namely, but not limited to, to give the notice of keeper liability in the format prescribed by section 9 (2) (f) of the Act. You cannot, therefore, transfer liability for the alleged charge from the driver at the time to me, the keeper.
There is no legal requirement to name the driver at the time and I will not be doing so.
I do not expect to hear from you again, or your debt collectors, except to confirm that no further action will be taken on this matter and my personal details have been removed from your records.
Yours etc
If you appeal online, make sure you do not tick any boxes etc. revealing who was driving, and check your spam folder for the response. If by post, send it regular first class, getting a free certificate of posting from a post office.