So the repair man has fixed the washing machine in a grand total of 13 minutes, including shifting the machine in and out of it’s slot (expert tip here, put two trails of washing up liquid in front of the machine to get it to slide better :)).
As with our earlier speculation it was a simple job. The repairman said it could really only have been one of two items – either the motor (a big job), or the control module. It being the control module it took longer going to the van for the part than actually replacing it, and most of the visit was taking the top off the machine, and looking up our extended warranty on his laptop computer.
He left the failed module with us, and pointed out the blackening around one of the contacts where the component that had burnt out was attached to the board. Having said that, this was the only evidence of anything having shorted out, aside from that the module looked fine. I asked him whether anything in particular could have caused it, but his response was that there was nothing in particular, it just happened, and that it was normal to just replace the entire module.
Slightly worrying considering that the washing machine mixes electricity and water, but anyway, we now have a fixed machine.