I'm having a moment of self-doubt. Just need confirmation that I am on the right track.

One of our vans stopped on a double yellow. No kerb markings, no plate.
He was making a delivery.
I sent the delivery note to the council involved.
They rejected our representation and said:
I would advise you that under the Traffic Signs Regulations and General Directions there does not have to be an upright sign stating "no waiting at any time" where double yellow lines are enforced".

I was convinced that if there is a double yellow line with no kerb markings you can load/unload.

What have I missed?

Without seeing anything other than this narrative, it would appear, nothing the council have disregarded your claim of loading, If it goes to appeal ask for costs

Please post copies of your reps and the rejection.

How long was he observed?

Not quite as long as we ever have to wait for Jo to comply to forum etiquette and actually show docs/give the necessary
details, in any thread.

Yes, that's a pop.

Was there absolutely nowhere else he could have parked to make the delivery? Or is this just typical delivery person laziness?

No kerb markings and no white "No Loading" plate, loading exemption applies.
As long as he was loading and can prove.