@Slim07 I think people are making this way more complicated than it needs to be, here's a simple representation:
Dear London Borough of Newham,
I challenge liability on the ground that the alleged contravention did not occur. I leave a van from DPD but on this particular day I was not working, rather I was taking my 14 year old son to buy some clothes for a wedding, I attach a copy of the blue badge and a receipt for the clother.
I trust that in light of this evidence you will cancel the PCN.
Yours faithfully
Send it off with photos of the clothes receipt and the blue badge (don't bother with the other bits of evidence at this stage) and let's see what they say.