1.3 carb cutting out at speed

I saw a few previous threads on a similar theme, but none seemed quite the same symptoms, so thought I'd mine your collective expertise…

My car (1.3 carb model) recently starting completely cutting out, normally when I've been travelling steadily over about 50mph for a while, but not exclusively.
No coughing or spluttering, just full chat to zero revs, but then straight away firing back up again, then the coolant light flashes at me for a few seconds as though the ignition had been off and on. The car then carries on fine as though nothing had happened.
It's been getting steadily worse, cutting out for slightly longer and more frequently.

I had a few suspects, fuel blockage/pump problem (but would that make the ignition go off and on again? and would it be so sudden with no spluttering?) the fuel filter seems clean, although I'm going to change it anyway tomorrow. I also suspected maybe the coil,  but I'd rather not buy a new coil if there's nothing wrong with it! Or just a loose connection somewhere in the ignition system, but can't find anything.

I also found oil in the air box, which seems to be a common problem from my internet searching! But figured it's unrelated.

Finally I realised it started happening not long after I changed the dizzy cap, rotor arm and HT leads, I was a bit disappointed with the quality of these items, do you think cheap leads or dizzy cap could cause the symptoms?

If the ignition is switching off it could be the ignition switch??

hmm, hadn't thought of that, thanks, another one to the list, the possibilities seem endless! Intermittent faults are a pain….
It does seem to be pretty consistently happening when I'm going over about 50mph though, only occasionally happening when I'm going slowly. I guess ignition switch would cause it to cut out at any old time.

lol another one! ive been plagued by the same fault! so far ive replaced the fuel pump, wired it in with a direct relay feed from the battery, tweeked the pumbing, had the fuel tank feed out, blown air through the lines, and cleaned rebuilt the carb some dozen times now!
im now at the point where it only cuts out on long throttle openings up hill. mine seems to be fuel starvation but i cant find the fault.
good luck

check the wiring to your coil is not under tension, i swapped mine but put it in wrong, so when the engine rocked it yanked the leads causing it to cut out.

Well this hasn't happened for a week now, so I'm hoping it's fixed. All I did was change the HT leads for some better quality ones so it seems the cheap leads were the culprit.