Thanks Andy. You're right, the red is definitely the earth. The red wire is clearly earthed to the metal chassis of the projector.
There is an in-line switch in the cable so I thought I would open it up to see which of the other colour wires was switched, implying that it would be the live wire. The good news was that the red wire was connected to a chromed brass plate around the bakelite switch, further confirming that it is the earth, and that one conductor was switched and the other not. So far so good.
Unfortunately the bad news is that the unswitched conductor is connected to the black wire at one end of the switch and the grey wire at the other. This presumably didn't matter in Germany as the plug could be inserted either way up. But it matters here, so I will borrow a multimeter and check which colour wire is the live feed to the lamp.
Thanks to everyone who replied.