Hi Ben
Do you have any idea as to what the make / model of your distributor? Is it a Lucas or a Ducellier?
Throughout the life of the A series engine, many differenent distributors were fitted, some a fully electronic, other use traditional contact points whihc open and close and these need to be correctly adjusted to have the right gap between them to stop them from be constantly closed and arcing which would also cause it to get hot and possibly melt plastic.
I'm not sure what the "red plastic bit" is that you talk of, I take it that if it keeps melting you have been replacing it, what ti the part called / part number?
All distributors will have a rotor in the centre under the cap, this has a metal strip running from the centre of it to the edge and this strip needs to be clean with no corrosion / dirt as it needs to make good contact with the relevent places on the cap.
When you replaced the contact set ( I think this is what you are calling a circuit breaker they are also know as points) you would have needed to connect a fly leed from them to a fly lead on an external condenser, or would have had a fly lead from an internal condenser that would have screwed onto the contact set, (which type you have will depend on teh make/ model of your distributor)
Either way the condenser is a small cylindrical thing, it is mounted externaly on the die nexed to the vacume advance on a Ducellier ,and it internal on a Lucas. A faulty condenser will cause the points to arc which will give of a lot of heat.
Acording the the Haynes Manual. the easiest way to test the condenser is to " remove the distributor cap, and rotate the engine until the contact points ate closed (put engine into gear and push buggy forwards / backwards to get the points to close) Switch on the ignition and seperate the points (ensure you took the car out of gear) (they points shoudl seperate as part of switching on the engine, this isn't a manual task for you to do) If this is accompanied by a strong blue flash, the condenser is faults (a weak spark is what you should see)
The most infallible test is to substitute a new condenser and check if the fault persists,
Simon