Do you know how far from the sign the No Loading restriction applies? There wasn't a marked bay that I could see.
Chalk and cheese I'm afraid.
In general, parking places allow activities, yellow lines don't.
Yellow lines can have 'No loading' signs, bays(when in effect) cannot instead they'll have 'Loading Only' with perhaps a time period.
If you couldn't see a bay then absent any photos it's reasonable to assume there wasn't one. Therefore this is strictly a yellow line and loading issue.
However, 'No Loading' on its own is not an approved traffic sign because its meaning is conveyed by kerb 'blips' alone - see items 1-4 of Part 4:
https://www.legislation.gov.uk/uksi/2016/362/schedule/7/madeWe really do need photos to unravel these contradictions, so over to you.