One hot pipe on radiator but radiator is cold

Albermarle

If I shut off one or both valves on a radiator here, the valves and pipes remain stone cold when the heating kicks in. The fact that one of the valves on your radiator is getting hot suggests that there is some flow of water through the radiator.

It is a good point. My radiators are the same. If one of the valves is switched off , the inlet and outlet pipes remain cold.
The radiator I had similar problems with as the OP, the inlet pipe and the valve body also got hot, but the radiator did not. Turning the L/s valve on and off several times and bashing it, eventually solved the problem, so I can only assume that was the issue.