Well, it seems I got my wish. I went down to the car park to watch it 25 minutes after I locked up and the wipers and indicator were going. I waited around and they wouldn't stop. With all that going, I couldn't lock the car by remote either, but I could unlock it. I locked it all with the key, then opened the bonnet and disconnected the battery.
The next morning, as soon as I connected the battery it started again (though it had swapped from the right to the left indicator!). With the ignition on it behaved itself, but once I parked it at work I had to disconnect the battery again. I booked it in with the dealer, but when I got home it had stopped (@rse!), but sure enough it started half an hour later.
The dealer couldn't work it out and had to contact Ford, and they said to replace the junction box on the Generic Equipment Module (GEM). That had to be ordered in, so I've spent a few days going to work by choo-choo.
Anyway, that seems to have driven the demons out for the moment, so we'll see if it lasts.