Yesterday I woke up in the morning to find the ring mains all dead. A process of elimination showed the fault to be the dishwasher, even when its programmer dial and front-panel switch were at the off position - which they'd been in since the machine was last used around a day earlier.
There was no fault with the 13A socket itself (it worked fine with something else plugged into it).
Google suggested the fault might be in the dishwasher's mains RF suppression capacitor, so I got the dishwasher out from under the worktop, and explored it until I found the relevant wiring.
By then the machine was tipped up, for easy access, and because there's not much working space in the kitchen at that point I had the dishwasher plugged in (when needed) to a 13A extension cord running to a more convenient 13A socket.
I couldn't then replicate the RCD trip. I also checked the wiring loom from machine's body to door, and the water heater though I didn't think either were likely to be the cause on a machine with switched off controller and power switch (unless they were faulty too). I tried a bucket of water tipped into the machine over the element as well. Still no RCD trip.
Hmmm. Surely it couldn't be a problem in the plug? But it was. There was a cremated caterpillar, about 1/4" long between the earth pin and the nearest edge of the fuse holder.
So, I feel like a fool for not checking the plug much earlier, but I also feel some sense of victory for avoiding a call-out fee to a local repair person whom I'm not convinced would have found the problem either.