I think you have procedural impropriety grounds of appeal arising from the NOR.And in any event you're at adjudication, so put forward every argument.
The NOR:
1. Does not inform you correctly of 'the form and manner in which an appeal may be made';
2. Misstates the council's power to increase the penalty.
3. Proves that the authority failed to consider your reps as required.
Both 1 and 2 are contingent upon a period specified in the regs, namely the 28-day period, also known as the payment period. This is defined as:
The period of 28 days beginning on the day of service[of the NOR].
The NOR in this case defines this as 'within 28 days of the day of service'. In plain English this means 28 days from the day of service.
This is wrong.
Furthermore, your rights of appeal fall into 2 distinct categories: your statutory right and the adjudicator's power (to accept appeals made late). The NOR not only misstates the statutory element, it omits the second completely, and compounds this by stating, incorrectly, that once the council's in its infinite ignorance serves a CC 'at this stage you have no further right to appeal'.
But you do, You have the right to ask the adjudicator to accept a late appeal.
As regards 3, I refer to the authority's reasons which amount to no more than that because the PCN was issued correctly they will not cancel. This is contrary to their obligations which are to consider your representations as well as the CEO's notes which by their very nature cannot deal with matters unknown to them, in this case you being in a nearby shop in the process of registering.
The authority is required to consider your and the CEO's cases, exercise judgement within legal and policy parameters and make a decision. In this case, did what you were doing fall within the legal requirement that a motorist is allowed a reasonable period in which to comply with requirements and that this does not obligate them to remain by their vehicle? There is no evidence that the authority made its decision in accordance with its legal obligations.
In my opinion.