Yesterday evening I was cruising in my Mk1 along a motorway at about 60 mph when there was a sudden, loud and sharp POP from outside and underneath the car, seemingly from somewhere on the nearside. My immediate thought was that a tyre had blown so I took my foot of the throttle, but nothing more happened, the handling remained completely normal. I then thought that perhaps I had burst a plastic bottle in the road, but a few moments later I heard the same sound, only this time repeated and much quieter - pop-pop-pop, pop-pop-pop. This time it seemed to be coming from somewhere around the rear of the car. Again there were no other adverse symptoms, the car continued running and handling completely smoothly. I drove rather cautiously for several miles but nothing else happened and I was able to complete the remaining 50+ miles back home without further problems. As far as I can see there is nothing externally the matter with the car, so I’m baffled as to what the cause of this noise might have been, I can only think that it must have been some kind of backfire, but I’m slightly concerned lest there might be something still undetected which might suddenly jump up and bite me. Can anyone offer any suggestions as to what may have caused this?
Normally exhaust ‘pops’ are unburnt fuel in a hot exhaust getting extra oxygen from a leak/pinhole. Happens on the overrun when the throttle is shut off and the exhaust pressure drops suddenly.
Tends to happen more if you are over fuelling. Could be an injector fault.
Check your exhaust for leaks, especially near the manifold.
I tend to agree with Hilux’s over-fuelling suggestion as being most likely. It could wreck the cat.
However there might be a mechanical problem. Many years ago when in my old bitsa with the hi-tune Kent engine there was this sound as if having run over a tin can, and it did not quite feel the same afterwards. A mile or so later, still several miles from home we went over a speed bump very slowly and there was this appalling BANG BANG BANG BANG from the engine and I killed the ignition. We towed it home behind the old woody mini traveller!
When I took the head off the engine I could see where an air-cleaner mounting nut had fallen through the carb and embedded itself into the piston. Two very slightly bent valves and several hex prints on the crown of the piston were further evidence.
Three hours later, two new valves and head gasket later it was running again. No longer with chamber capacities perfectly matched, but compression pressures still within a psi.
A dome of stainless steel mesh (stolen from a kitchen sieve) fitted between carb and air cleaner frame acted to prevent any future loose nuts falling through.
Shotgun fire by any chance ??
Just a thought. 
Akin to an episode of Midsomer Murders.
“It assumed it was just a car backfiring, until I found the headless corpse in my paddock!” - Ms. Margaret Dunstable.
Thanks for the above replies. The shotgun suggestion may not be so far off! I’ve since had a word with my regular mechanic (who also has an MX5), who said that the complete absence of any kind of reaction from the car leads him to think that it was a plastic bottle or similar debris, which burst under the front nearside wheel. He thinks the remains were then thrown up towards the rear of the car, where it briefly became trapped and fouled the rear wheel or some other moving part before dropping free.
Since it happened I’ve driven the car for several miles locally without incident, so I think he might well be right. In any event, he will be getting the car through its MoT in two weeks’ time and will make a special point of checking any suspect areas.
I know it sounds crazy, but I had something similar happen to me.
A crack, folowwed by a crack crack.
WTH was that ???, then realised either someone was shooting pigeons or clays in the wood opposite.
My initial reaction was the car.