Well, it's gone back to
LCE who will pass it on to Canon for a fix. Fault reproduced on multiple lenses, with a different battery etc. Power would blink off briefly and then either come back straight away, or trigger a sensor clean and seemed to happen on occasion if I tilted the camera a certain way. Battery capacity also showed odd jumps up and down for between 5-10% for no obvious reason. So I'm guessing an internal power issue.
Hopefully Canon can quickly fix it. Does anyone have any experience of warranty turn-around times when it's a retailer sending it back? I'm a Gold CPS member, but obviously that won't help in this case, I assume.