How about this:
Dear Hillingdon Parking Appeals and Processing,
I am writing to ask you to exercise your discretion and cancel PCN No: HN24219947 against VRN: Y200WLD.
[My address etc.]
The facts of the PCN:
The PCN was issued at 12:59. The parking restriction ended at 13:00. The first evidence photograph taken by the CEO of the car with the PCN attached is timestamped 12:59:42 (18 seconds before the restriction ended). The final evidence photo taken by the CEO is timestamped 13:00:04 (restriction no longer in effect).
My appeal:
I made every effort to comply with the restriction. I checked the signs and then my car's clock, which indicated that the restriction was just about to end. I then spent around a minute unloading my vehicle and walked away, believing that enough time had elapsed and that the restriction had ended.
I have a medical condition which means I sometimes move slowly, therefore I believed the time I spent unloading would have been ample for the restriction to end. There were several other vehicles already parked on the same single yellow line when I arrived (shown in the CEO's photos), which reinforced my reasonable belief that the restriction had ended.
I believe I may even be visible walking away from the car in the top left of the evidence photograph taken by the CEO at 12:59:42 (18 seconds before the restriction ended). It was raining at the time and it is clear from the wet road underneath the car that it has been parked for moments.
Summary of mitigating factors:
I have never before been issued with any form of penalty notice. I am a law abiding citizen and took every effort to comply with this restriction.
I believe any contravention lasted, at most, seconds. I do not understand how the CEO can claim to have observed my car from 12:55.
There were several other vehicles parked on the same single yellow restriction, all visible in the CEO's photos. None of those vehicles appear to have been issued with a PCN.
[Kind regards etc.]