I've managed to get the broken end of the crank off the shaft, at least. I close examination suggested that I might be able to make out the end of a thread on the inside, so I put it in a vice and turned the broken bit with a pair of mole grips. It came off nicely.
I don't think I can repair it. It's sufficiently small that I don't think it would survive an attempt to braze/silver solder it (assuming that's even possible with aluminium, which is what I assume it's made of). If I can identify the thread (it looks far too coarse for a standard metric thread, but I seem to recall there are some common coarse sizes) I may be able to make a new one from a bit of scrap.
James