Well... let me bring you all up to date. I tried the extension lead thing - that was uneventful as nothing tripped, same with swapping the two 32A MCBs. The next thing that happened was that the dishwasher wouldn't turn on. Everything else on the circuit was still on. Decided to try swapping the fuse, and on plugging it back in (with my head in a small space between the machine and the socket at the back of the recess) there was a very loud pop (fresh underwear please) and an overheating smell. I recognised that loud pop from when the circuit tripped once before when I was in the vicinity.
So I pulled the dishwasher all the way out and had a look at the back. The white plastic plate over what is presumably the power unit, where the mains lead enters the machine, had yellowy-brown discolouration around it and had that look of overheated plastic that you might see on a light fitting. What's more, the coating on the back panel of the machine - some kind of black hard foam stuff - had melted in various places, and I could see where the corrugated waste pipe had been touching it (and exposed the metal underneath).
Funnily enough, we haven't used the machine since. And funnily enough, nothing has tripped since. I really thought the story would end there, but at the weekend we decided to shuffle things around a bit and moved the small freezer to the socket which the dishwasher had been using. At this point I found that the socket was dead. So currently the freezer is sharing a 2 way extension lead with the washing machine :/ (the two haven't been used together yet) and I'm wondering what the heck is the matter with the socket, which is all of a couple of feet away from the washing machine socket. I've not had chance to open it up and have a look, but if anyone has any theories before I get round to it, feel free to air them, it'd be much appreciated as ever.