So I put the spare wheel, which is in much better shape, in the troublesome front left position, used a spare wheel cover and put duct tape on the rim and it seems to be all good now - the wheel cover has found its groove and is staying in place. The only trouble, of course, is that I did three different things, so now I'm not sure which one actually fixed the problem! Just changing the wheel with the same cover didn't work, so I suppose it was either the different wheel cover or the duct tape (or both).