You have no idea what administrative process might have preceded the issue of the demand though... The "computer generated" aspeect is really of no consequence, though I can imagine your views if you'd received a demand painted onto vellum and delivered by a courier on a horse, weeks or months hence... ;-)
Have you never seen any of the TV programmes showing C&E staff dealing with the mountains of parcels in a depot, investigating some... Why would you expect it to be quick? Surley they have a stack of stuff to work through.
A week strikes me as pretty reasonable. Remember, it's you who chose to buy something from another country.