You certainly can submit representations against the PCN to the council, and if all reps are refused, the right to appeal to the Traffic Penalty Tribunal.
However, from your narrative, any argument you would put forward would be on the basis of mitigation, (arrived in the dark at 2 am, tired, unfamiliarity with the permit system, etc). Acceptance or rejection of this basis is entirely within the council's powers, the TPT adjudicator can only decide on the basis of the statutory grounds for cancellation. Mitigation is not one of these.
So it's essential that any reps you submit are non-confrontational, as you are trying to persuade them to give up the sum of £25, (the discount from the full £50). If they refuse your reps, they will re-offer the discount if you submit them within the discount period.
