As above... Plan A is always to get the landowner or their managing agent to get the Parking Charge Notice (PCN) cancelled.
The only caveat is that as the Keeper who has received the PCN which was sent as a postal Notice to Keeper (NtK), Britannia has no idea who was driving. The Keeper and the driver are separate legal entities and if Britannia has not fully complied with all the requirements of PoFA, then they cannot transfer liability for the charge from the unknown driver to you, the known Keeper.
When you make your complaint to Waitrose, you do so only as the Keeper who has received the speculative invoice from the unregulated private parking company. Only refer to the driver in the third person. No “I parked here or there”. Only “Themdriver parked here or there”.
However, please show us both sides of the NtK you received. Only redact your personal info and the PCN number. Leave all dates and times visible. This will allow us to advise on what steps to take for plans B, C and D if plan A does not work.