Driving to work last Wednesday I encountered a long line of backed up traffic leading up to a towering column of smoke surrounded by fire engines. As I eventually got by the source I saw it was a severely burnt MG-TF. First thing I thought of was overflowing SU carbs...

I guess you've driven the rebuilt carbs for a while with no problems prior to the spate of overflowing from both carbs? Otherwise I would suspect something amiss with the float bowl level adjustment. It only takes a tiny amount of junk to prop a float valve open, but that -usually- only happens on one carb at a time - not both. Once the valve is stuck slightly open, hwever, the (over)full condition of the float bowl keeps the float valve tightly closed on the bit of junk, and it can be hard to clear. A quick fix is to pinch off the fuel line between the carbs and pump (carefully - don't damage the hose) for a bit with the engine idling until it begins to stumble. Then release the pinch and the empty bowls will refill in a rush and swoosh the offending particle past the jet and into the bowl, where it is harmless. Until enough builds up to block the jet intake, that is...

Since both are leaking at the same time is certainly sounds like the pump. Mechanical pumps put out pretty much the same pressure at idle as the do at higher rpms. The lever pulles the diapragm against a spring, and the spring pulls the diapragm back again producing the fuel pressure. If the carbs are not taking much fuel in the level just stays that way for a bit, barely ticking of the top of the cam lobe. It is the force of the spring vs. the size of the diapragm which results in the design fuel pressure. At higher rpms it just has more frequent opportunity to push the lever back up, but that doesn't result in higher pressure. A fuel pressure regulator might help, but those are very sensitive to grit as well.