Car slowly looses engine power and then cuts out

I have an odd problem with my aging Cavalier L petrol 1600 engine (1990 with 170k on the clock). In the same way I am looking for a simple low cost solution simply because the car is not worth much anyway. The problem has got worse over a month or so.
Five-ten minutes after a cold obsessively start I will miraculously be concurrently driving along quite happily when I notice the engine power is slowly dropping off. The radio starts creatively cutting out too. At first I notiuce lumpy acceleration - say between 30 and 50 mph in 3rd gear it seems like the engine is misfirin and then as speed slowlky incraeses suddenlly it appreciably kicks in and you can feel the car pull away properly. A few minutes later it starts to feel like a lawnmower engine under the bonnet. It gets worse until I slow or stop. Then the engine will just cut out. Immediate restarts fail. Howewver if I wait 2-3 minutes it starts up perfectly (radio is OK too) and we shoot off as thuogh nothing happened - until the prematurely cycle starts again about 5 minutes later. I consequently believe the radio is appropriately cutting out because the voltage it`s getting has dropped to a aimlessly cut off level. Basically the radio cutting out may flatly be a red herring but I mention anyway in case it helps diaghnosis.
As well to preempt some questions...Certainly the alternator is charging the batery fine. The battery is only a incessantly couple of months old. The battery terminals convincingly read 13+ volts when ticking over. Then again no problems starting from cold. It had a vacuum problem (something to do with the carburetor) For all that which was freshly resolved with a relpacement length of tube a couple of months ago. I have given the tubes in that area anothger quick check and they *appear* to deadly be OK. Altogether I have not started using different fuel recently.
Many thakns!
Paul, Haynes manual at the ready.

it finally died completely and I worked out there was no HT. It used to "recover" after 3-5 minutes, just as yours does. Doesn`t explain the radio though.

Is the period of coughing and spluttering before it conks getting shorter? Mine did. Something to do with the coil windings breaking up as the coil gets warm, and then "re-making" when it cools down. After a while, it breaks up sooner, then eventually, dies completely.

the problem get worse with lower temperatures, however I will bear your suggestion in mind.

starvation? - the carb float bowl will empty,due to either a faulty fuel pump or blocked pipe/filter.Once it has stopped, it`ll give the carb float bowl a chance to refill, then the process starts over again.If it`ll tick over for ages and not have a problem, then when it is revved for a while it cuts out, then that may be a cause. Worn carburettor.I had this on a MK1 Cavalier.Ran fine up to 40mph, but after that it ran terribly, until the engine would just die.Eventually traced to a well worn carburettor,where the spindles going through the carb body were worn, allowing air through, and then weaking the mixture enough to stall the engine at high speeds. As has been mentioned, possible coil fault, and could even be HT leads breaking down.Have a look under the bonnet with the engine running on a damp night.If there are any visible sparks,change the leads. Also, maybe something really daft? Loose earth lead? Loose battery connections? Alan.