The reverse side of the PCN pl, your initial reps as written, not a summary, and their reply.
The contravention is that you 'Parked in a car park etc.....'. On its face this has nothing to do with whether you displayed a BB or not because the default position is that your BB applies ONLY to a road, not a car park.
Whether you were permitted to park in the car park without paying the charge is determined by looking at the Ts and Cs of the car park.
Places you need to check before parking
There are a number of restrictions and local parking schemes which you need to be aware of. Here is a list of those places and the parking restrictions in force. If in doubt, ask the relevant council before you travel.
Off-street car parks (such as supermarket, hospital or local council car parks)
Off-street car park operators should provide parking spaces for disabled people. However, it is up to the car park owner to decide whether badge holders can park free of charge.
Do not assume you can always park for free.
Unfortunately, the GSV vehicle couldn't negotiate the height restriction, so what are the conditions of use pl?