Naturally, we mopped up the spill (while I shouted at her!) and I unplugged the machine. However every time I turned that ring back on, the RCD tripped. There was no way water could have reached the sockets (they are above the machines) and there are no junction boxes under the floor that could have got wet, so no obvious reason for the problem.
I started to unlug anything on that ring and found the tumble-dryer's moulded-on plug (dryer was not in use) badly melted and very hot. Further investigation showed the pins to be bright and clean and totally unmarked by heat. The front of the socket was also damaged, but internally was fine. It appears that the overtemperature has been on the fuse clips or their rivetted connections. While the body of the plug is badly melted and distorted, the fuseholder is blackened, charred and badly out of shape.
Both plug and socket replaced today and everything seems to be running cool.
Very odd that both events should occur simultaneously, but without the dishwasher tripping the RCD, the tumble-dryer plug could easily have started a fire - especially being close to a basket of already dried clothes.
Very lucky escape.