Alarmingly, once I reactivated the plugins, they all worked and the sites have not disappeared. I suppose I should be pleased that it’s all working again, but there’s something unsettling about not having pin-pointed what caused the problem.
It was a plugin, although I’m not sure which one at this stage. I renamed the plugins folder and everything started to work, now I’m going to reactivate them one by one and figure out which one was causing the problem.