Because I don't trust anyone, I called HiSense again. Seems they also wanted a photo of the serial number, but weren't going to tell me. I may have imagined it but the agent seemed surprised that not only did I have a photo, but I could send it by return which I did.
I'll call again in half an hour to see that they got it and push things forward.
Many thanks again for the support.
It seems that once I have this uplift number, I can relax a touch ? Nice recorded delivery letter to Currys outlining this saga. (The temptation to give them a collection time of 8am-8pm and be out when they call is powerful.)
What galls most is if you listen to the recording of the first call I made to HiSense when I asked "What if the engineer doesn't show ?" I was told quite brusquely that doesn't happen. I bet they "can't find" that recording.