Before we go any further, it would be useful to clarify who you mean by "we" - the notice will be addressed to the registered keeper, an individual (unless your vehicle is registered to a company?), and it is that individual who must submit any appeals etc.
The good news is that Smart Parking are easy to beat. They make no effort to comply with the requirements of Schedule 4 of the Protection of Freedoms Act (there's a link in my signature), the only mechanism that would allow them to hold the registered keeper liable. Without complying with that, they can only hold the driver liable, and they don't know who that is.
The registered keeper can appeal as 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").
There is no obligation 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 the charge has been cancelled. If you choose to decline this appeal, you must issue a POPLA code.
Yours,
Appeal online, being careful not to tick any boxes that reveal who was driving, the appeal is being made by the registered keeper.
Keep an eye on your spam emails for the reply.
The above appeal has a 100% success rate with Smart Parking so far.