Generally only newer thermostatic rad valves (TRV) have an off position. Generally the lowest setting is "Frost" so if the room is cold, they will not switch off. Of course, it may not be working properly and allowing water to pass.
Certainly, more oil will be used if the rad is hot, but how much depends on many factors such as the outside temp, the efficiency of the boiler, the size of radiator.
It is accepted that at least one rad must be left on permanently to protect the pump.
Personally, I do not believe leaving the heat on 24/7 is the most cost effective way to heat a house but prefer to heat the rooms as and when I want. There are many though who will argue this point.
With a TRV setto zero it stll allows an amount through it, as diyers have found to their cost after removing a rad.
If you have the caps that came with the valves they WILL turn the rad off.
You need to remove TRV head first.
It maybe that the radiator is on because it is a bathroom with an outside wall although there are two bathrooms side by side and the other is not on. Even if I put rad on 2 or 3 setting it is belting out as if on 6. When I said rad was off I did mean frost setting. I did not realise that one had to be on all the time to protect the pump - does the frost setting count as on?
Do you think it is a problem with the thermostat on that rad and a plumber could sort it?
It sounds as thought the TRV is faulty. I would suggest you have it replaced as the modern TRVs will close the flow completely. Frost position does not constitute a by pass to protect the pump and boiler. Ask your plumber to check if there is a by pass built into the system pipework.
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