I've just seen a triple-LED light source with a pencil-thickness flexible shaft about 6" long, in a tool shop window. About £10. Can't see that I'm going to find anything better than that, so problem solved, thanks guys. I can tape it to the router body and aim it precisely where I want the light.
Please don't tell me you've seen the same in your toolshop window for only a fiver!
Regards, John