Your lease company have acted wrongly here. The Notice to Keeper (NtK) clearly states:
If the vehicle has been hired, please provide us with a signed statement confirming the hirer's name and address and include a copy of both the hire agreement and their statement of liability, as required under the Protection of Freedoms Act 2012.
Instead of following that process, they sent a Letter of Authorisation (LoA). That is not what PoFA requires, and if the operator refuses to accept it, liability remains with the lease company which means they may end up paying it and charging it back to you.
They have also wrongly referred to this as a "Penalty" charge notice. It is nothing of the sort. A penalty can only arise from a statutory authority. This is a civil matter, and the notice is merely a speculative invoice alleging a breach of contract by the driver, issued by an unregulated private parking company.
You should instruct your lease company to transfer liability properly, in accordance with the NtK and PoFA. Once they have provided the operator with the hirer’s details, a copy of the hire agreement, and the statement of liability, the lease company are absolved of any liability. The operator must then serve a Notice to Hirer (NtH) in your name.
When you receive the NtH, you should appeal only as the Hirer. Operators rarely comply fully with PoFA in hire situations, meaning liability cannot pass to the hirer. Only the driver could then be liable, and the operator has no evidence of who that was unless the Hirer discloses it, inadvertently or otherwise.
Once you receive an NtH in your name, use the following as your appeal. No need to embellish or remove anything from it:
I am the Hirer of the vehicle and I dispute your 'parking charge'. I deny any liability or contractual agreement and I will be making a complaint about your predatory conduct to your client landowner.
As your Notice to Hirer (NtH) does not fully comply with ALL the requirements of PoFA 2012, you are unable to hold the Hirer of the vehicle liable for the charge. Partial or even substantial compliance is not sufficient. There will be no admission as to who was driving and no inference or assumptions can be drawn. Bank Park has relied on contract law allegations of breach against the driver only.
The Hirer cannot be presumed or inferred to have been the driver, nor pursued under some twisted interpretation of the law of agency. Your NtH can only hold the driver liable. Bank Park have no hope should you be so stupid as to try and litigate, so you are urged to save us both a complete waste of time and cancel the PCN.