Thanks Laird Scooby. I now have the Top Gun music playing in my head....
Finally got to look at it last weekend, lots of corrosion on the contacts inside the dizzy cap and on the rotor, no or very weak spark on all cylinders except one. There's a broken bolt too, so the cap isn't held on properly - so explains moisture getting in. Cleaned actual chunks of corrosion off the contacts - still no joy starting, but then I've removed a good few mm from the workings which is bound to have an effect.
Probably could have got away with a new cap and rotor (the coil seemed OK), but found a new replacement dizzy for not a whole lot more, so ordered that. New HT leads and plugs too for good measure.
Definitely getting fuel and it's not the immobiliser, so hopefully this fixes it.
Have reached an agreement with Whatserface, I'll be keeping both the FTO and the Honda (which are the most important things), and a 50% share of both children.