So what to do? We first rang Miele customer support. No problem, they say. Call out £98 for the first hour plus parts plus VAT. Nice. Then they say we can sign up, for £200, to a 12-month warranty and have it repaired. Nicer. But then they said that my machine was too old (it wasn't - the girl had mistakenly interpreted the warranty). Still too expensive though.
What next? Out comes the laptop and off we go(ogle). Interestingly I found this thread on DIYnot eventually which seemed to match my symptoms. Looking at the potential cost of parts (under £5) it was well worth attempting the repair myself - even if that didn't fix things - so I ordered a fuse and a relay and fitted them both to the controller board (the fit took less than 15mins) and we now have a working machine. And I now have a happy wife.