Well, it looks like this is a batch/model problem.
AO.com replaced the microwave for me, and arrived bang on time, very efficient. However, the replacement is also broken.
The previous one died totally on Christmas day. We did try the turning it off and back on trick, and even waiting a few minutes, but no joy, no display. Before the replacement arrived I doubled checked it was still dead, and it was not - it worked. So I tried the pop-corn for 3 minutes test. It failed.
However, to my shock, the replacement was the same.
I am worried AO may not believe me, or consider that I don't know how to drive a microwave, so this time I made a video.
But, obviously, I may be expecting too much. I don't think so, as I had the older model of this microwave, also 1000W, and 3 minutes was fine for pop-corn. The bag says 1½ to 2½ minutes for 950W. But lets be scientific here...
I used a cheap tesco own brand 650-700W microwave. The bag says 2½ to 3½ minutes. But 3 minutes created a full bag of nicely popped corn with no problem at all. I also made a video.
So, waiting for AO to reply to that.
Update: Got a helpful call - they agreed swapping to a different model would be sensible, and went through various models with me. It will arrive tomorrow. Very efficient - actually quite pleased with AO now.
Update: Got an Electrolux EMS30400OX, seems to work a treat.