If you want to stand your ground, you must now wait for the Notice to Owner, sent to the name and address on the V5C Registration Certificate for the car. Is this you ? Please let us know if it isn't as this complicates matters.
Assuming you are the owner, on receipt of the NtO , you then submit formal representations, accompanied by evidence, (photos). At this point, the discount option is lost, but on the other hand the penalty doesn't increase any more, so if they refuse you, you register an appeal at the Traffic Penalty Tribunal, which would be a PITA for them, as they would then have to prepare an evidence pack and find out, no doubt, that your evidence is correct !
It all depends on your attitude to risk.