So, I found the ground by the battery on the left hand side of the car (you know, the side where the passenger would <i><b>normally</b></i> sit), and gave it a good clean and that did the job (Thanks Mildred).
Well, it sort of did the job. The wipers spluttered very slowly into life and stopped, so the ground wire must have only been 1/2 the problem.
Fiddling around I saw three multicoloured wires going between the body parts of the wiper unit. If I gave these a bit of a tug the wipres started to work again. I'm going to pull the motor off at the weekend and see if one of them is loose in any way, or if there are some contacts that need cleaning.
One thing I've noticed is that the wipers don't have much power. the second the windscreen starts to dry they really struggle to move. Is this normal?