Well, it wasn't the battery. Which died, on Thursday of last week, with no warning. The dash lit up, but the engine would barely even crank.
I replaced that (and I'm not dead! Yay, go me!), and as a result, I now own a few small spanners (7mm, 8mm, 9mm) and a small socket set.
The old battery was a Yuasa and was 9 years old, so it had been fitted when the car was between 3 and 4 years old. I replaced it with a Yuasa HSB012 Silver 5000, which has a 5 year guarantee. £90.
The fault hasn't cleared, so that knocks that idea out. The next step will be replacement of the throttle body. I do have the PP2000, but haven't got round to finishing the setup yet. I can't really afford to replace the TB yet, I'll get the PP2000 up and running, read the faults, and see what it says.
This is the cheapest I've found the throttle body so far:
http://www.bestpartstore.co.uk/1858014