I have had the benefit of reading my colleagues reply and I agree with the comments therein. I have also read the notes and agree with you that what you are doing would potentially come under the auspices of the Securicor analogy.
If there is no loading or unloading then it doesn’t matter why, because it is an absolute prohibition.
The difference between the Securicor issue and the pizza is one of not necessarily value but also weight in relation to money and volume in relation to the number of pizzas.
Clearly, it is unreasonable to expect security guards to carry heavy and valuable money long distances from wherever they would normally park with no yellow lines to wherever they are effecting the delivery.
In your case, carrying one pizza is less of a problem because of the weight and value than carrying money. If however there were dozens of them, the situation is different.
What you have to remember is that even if we give you an opinion which says that you can park on double yellows (with no loading restriction) and deliver your pizzas, even one pizza , if you have an enthusiastic traffic enforcement officer who decides to pop a ticket onto your windscreen, you are then faced with defending the PCN and it doesn’t matter what our opinion is if the judge takes a different view. Solicitors do not always win when they go to court.