Imp engine cutting out once warm

I had strange symptoms on my Imp - turned out to be inlet manifold loose on head so allowed air leak.

Thanks guys I'll try these things for starters (one at a time) and let you know results. Plug gaps first as that's super easy, I'm set to the book gap wise but a touch closer wouldn't hurt.

I'd check your rotor arm first TBH. My Beetle had a mystery cutting out issue as a result of this as have a few people on here. If you have an old rotor arm (i.e pre 1980s) arm lying around I would use it. OTOH the red items seem to be reliable these days. I would check for a spark with an spark spark plug to be honest.

Which Lumenition is it? The Magnetronic items seem to be fine but the connectors on the Optronic systems can play up. What dizzies do they run again?

How long in terms of time will the car run for once you take the choke off?

If the gaps are set to the book the car should be OK.

I noticed that you said your Imp is running a Weber Progressive carb. How does the inlet manifold stay warm on these? I would be tempted to see whether the carb or inlet manifold is icing up as well.

Coils IME rarely fail but are often incorrectly blamed. The spark test may potentially rule it out. Whatever you do, do not buy a County or £10 coil , they can cause more trouble than they are worth (BTDT) However, for me, it caused a non revving issue which was also partly down to the spark plugs. If you do have to buy one get a Bosch Blue or a Lucus Sports item which is a little easier on the wallet.

Which luminition?
What coil resistance?
Anything else in the circuit - rev counter etc. any eratic movement?
Does it rev or just not idle?
Have you pulled the the idle circuit jet and blown it through?