If you haven't already done, so, at this stage, you would be submitting an informal challenge. Be aware that 99% of these get a Fob-Off letter from the council, as they know from experience most people then cough up to get the discount. They do this because most people know little about parking law, and have a somewhat naive belief that councils act correctly at all times. Would that it were so !!
So if you really want to fight this one, after getting the inevitable rejection to your informal challenge, you would have to wait for the Notice to Owner that is sent to the name and address on the V5 registration certificate for the car. Is this you ? Assuming it is, you submit formal representations, basically the same as your previous reps but this time informed by what they said in their rejection. Reps against an NtO are normally looked at a lot more carefully, because the council now know that you accept the loss of the discount, so are more serious. However, a large percentage of formal reps get rejected, thus forcing you to London Tribunals. HOwever, councils are now wise to the fact that if they reject formal reps it is a no-brainer for the appellant to take them to adjudication as the penalty remains the same, and there are no extra costs. To counter this, and also avoid the fag of preparing an evidence pack, it is now commonplace for them to re-offer the discount to "encourage" payment. Of course if you take them to London Tribunals it is always with the full PCN penalty in play.
PS: You don't have to submit an informal challenge, but it is useful to do so, as you might get material that can be used against them. Councils ruthlessly game the system so we must, too.