Okay, I think I may have found the root of the problem.
It was niggling in the back of my mind that something wasn't right, and I did a quick google search and confirmed that the Red power light should not be flickering. On my pi it blinks off and on frequently. This seems to indicate a drop in voltage.
I tried switching the power supply to an official Raspberry Pi PSU (I was using a Samsing charger) but it's still doing it, particularly when the Edimax dongle is plugged in, I think. I will try to do some more experiments with different cables, but could this be a fault in the Pi itself? I'd appreciate any further thoughts.