I agree with the draft except for the key point of 'cancel the charge'.
If the OP is so minded, they could perhaps change "I look forward to your confirmation that the charge has been cancelled" to "I look forward to your confirmation that my appeal has been upheld".
Either way, Horizon's template response to the above appeal usually contains the line:
"I can confirm the Parking Charge Notice has now been cancelled"
If the driver was a genuine customer then they can approach Tesco and ask them to intervene, ideally providing a receipt from their shopping on the occasion in question (presumably quite a hefty one for such a long stay). Otherwise:
Any obvious grounds for appeal?
This being Horizon, they have as usual decided not to bother issuing a notice that complies with the requirements of Schedule 4 of the Protection of Freedoms Act in order to hold the registered keeper liable. Therefore, you could appeal as the registered keeper (being careful to not reveal, via any tick boxes etc on the online form, who was driving), 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 am appealing this notice on the grounds that I have no liability for this matter as the registered keeper of the vehicle.
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"). You have chosen not to issue a Notice to Keeper in accordance with The Act, and it is now too late for you to do so.
There is no obligation for me to name the driver and I will not be doing so. As I have no liability for this charge, I look forward to your confirmation that the charge has been cancelled. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
Keep a close eye on your spam folder for their response. If they do not respond within 35 days, chase them.