Thanks for the welcome.
I know I should have joined earlier but I doubt in this instance the collective wisdom would have been much help.
Proving that the AA were/are at fault is nigh-on impossible - until the root cause is discovered which will take too much time.
The car was working fine. My wife stopped at her parents house and when she came to restart it, it wouldn't. It would turn over but not fire.
I called the AA out and after much investigation and head-scratching the patrol-man decided to try a new coil. The car started with a new coil. The old one was too hot to hold.
Having started the car with the new coil 'hanging free' the patrol-man then fitted it in position against the bulkhead and attached the earthing strap. We then tried to restart the car. A burning smell and then puffs of smoke as part of the wiring loom melted.
So something was shorting to earth and bits of the loom were melted. Until the loom is repaired it will be v. difficult/impossible to identify the fault - which probably caused the original coil to blow.
We'd been thinking of changing the car anyway and have now bought a replacement so I will be disposing of it, which is a shame because I've enjoyed the car.
I will start a new thread in the appropriate section with photos. I just need some time...
In the meantime it is a 5 door 1998 Mk3 2.0l 8v GTi in British Racing Green. 114k miles with one "careful"

owner. MOT 'til Feb '11 and FSH.
I am sure that a keen/experienced auto-electrician will be able to fix the melted bits of the loom.