I suggest you delete the attachment with the medical report as you've left a lot of personal information in there (you need to send it to the council but you don't need to post it on here).
Anyway, here is a draft representation:
Dear London Borough of Bexley,
I challenge liability for PCN XL19984412 on the grounds that the alleged contravention did not occur. At the time of the alleged contravention, I was engaged in unloading, specifically I was delivering a heavy package to the post office as I was sending a 10 kilogram training vest to my son. I have also recently injured my foot and as a result I cannot walk very fast or very far, so I had to park reasonably close to the post office.
I attach a copy of the post office receipt, the receipt for the training vest I was posting to my son, and proof of my medical injury.
While I appreciate the CEO could not have known any of the above and he was right to issue the PCN, it is clear that the contravention alleged did not actually occur, so the penalty charge must be cancelled.
Yours faithfully,
Send this via https://pcn.bexley.gov.uk/TicketDetails.aspx and keep a screenshot of the confirmation page.