OK, so the factory reset, and re-inputting my info does seem to have cured the problem. I haven't done the firmware upgrade as yet - I'll try it for a while as is, and see what happens.
Interestingly, I've gone back through my old video captures, and now that I know what I am looking for, I can pretty much pinpoint the moment when the fault occurred. It was on the night of Saturday April 21st, at approx 10.30pm. We had just had dinner in a local pub, and as we left to drive home (no, I hadn't been drinking) there was a huge thunder/lightning storm. We drove up onto the nearby fells, and watched for around 30 minutes, as the lightning struck all around us. It was as we left there to drive home, that I noticed for the first time, that the live view had appeared on screen. At the time, I assumed that I had inadvertently changed something in the settings myself, as I had been videoing the storm, and had moved the camera a bit to change where it was pointing. However, I now believe that it was a fault caused by the lightning - not a direct strike obviously, but the atmosphere must have been so charged where we were, that it caused some disruption to the circuitry, and caused this fault. Only a theory of course, and impossible to prove, but I do have a background in electromechanical engineering, and in my experience, random electric currents of significantly lower power can easily nuke circuit boards and microchips, so I reckon that it's the most likely candidate.