So glad you found the problem in time!
The auto on/off is probably triggered by a motion detector. My guess is the motion detector malfunctioned. If that's the case, looking at the plug will not help B&D determine the problem.
I, too, have left my iron plugged in by mistake. Luckily, we haven't had a fire from it. I also have a silicon ironing pad to rest the iron on, and find that extremely useful. I think that it provides a bit more protection, since the silicon can handle much higher temps than the ironing board cover.