Earlier quoted context omitted.
The blank vans, oftentimes actually rental vans, are actually Amazon Logistics. This is Amazon's own delivery operation in the UK, and all Prime deliveries in my area use this service. It's been years since I have seen any third party delivery providers for Amazon orders.
Every time I've got something delivered by Amazon Logistics, it's actually been APC. Oh, and it's shit. Order next day delivery at 9AM Monday? Delivered 7PM Tuesday! Get it Wednesday because the post room in my office closes at 6PM.
Also, I live 100 yards from Currys/PC World and they're actually cheaper on a lot of things (which was a bit WTF when I discovered it)