I found this on Ealing's website:
https://www.ealing.gov.uk/download/downloads/id/15040/parking_code_of_practice.pdfI can see that boarding and alighting are exemptions from code 12 contraventions(res permit or shared use bays) but cannot find this for code 25, loading bays. Stamfordman's quoted decision relates to code 12.
Their reply doesn't help us because they've ignored/not comprehended the basis of your claim to an exemption.
In the world of money-grabbing councils, the burden is on you to establish that an exemption applies.
But how is the question. Setting aside prospective procedural improprieties, IMO simply stating that X happened* but without any objective evidence in support makes your task difficult. These cases more often than not end at adjudication with the full penalty in play and the appellant attempting to convince an adjudicator on the balance of probabilities that their claim is credible.
*- a blue badge isn't really central to the issues in this case IMO.