Not familiar with these cars. But
if the coil is going west, it will work when cold, then heat up till its getting to hot to touch. The is is caused by an internal resistance. The resistance grows greater as the heat rises. So if the coil gets hot in 5 minutes of the ignition being left on, suspect number one. Cannot fix this, a new coil.
Can be a capacitor, but that is a much more tricky thing to check. Only real give away is if you have points, they might be very pitted and burnt looking.
Fuel starvation. The after market filters can be the cause of this, especially on a gravity fed system. if fitted, they need to be away from sources of heat. If there is a pump, it maybe pumping ineffectively, and not able to keep up with demand. Might be some auto choke on the carb not turning off. If the filter is full, its unlikely, but the vent in the fuel tank or filler cap, is blocked.
These are general fault finding, and might not apply to your car as it might have contactless ignition etc etc. That is all mumbo jumbo to me.
Bristol is not far from the Bath Microcar Rally at Keynsham. Rugby Club in a few weekends time. Might be that someone there is knowledgeable on these cars.
Hope that might help.
