Sounds like a head gasket in any case.
But I can only recommend that the radiator gets flushed out, with water and compressed air, both ways.
I had persistent overheat problems in my latest MGF, especially at higher speed!! Fans were working (for radiator and also for the engine bay) did not lose water and heater hot.
Turned out the radiator was full of scale rust particles, I guess about two spoon full of them!!
After flushing both engine, engine oil and engine bay temperatures dropped.
I guess the oil temperature dropped about 10 degrees.
So definitely worth a try! I collected the water in a white bucket and it was easy to see what came out!!