There it sits, cable tucked neatly where the manufacturers intended.
How could I not have seen this? Traily wires really annoy me, and I did try to tidy it up with a twisty bag tie (worked....for three minutes).
I'm going to look around and see what other blindingly obvious little frills my domestic kit has up it's sleeve.
I am (a) thick and (b) concerned that it speaks volumes about my quality of life, being as delighted as I am about this discovery