if you turn off all the hot radiators, does the cold one then warm up?
if so, it is most likely because there is an easy passage of flow through the hot one(s).
If there is an easy path, them the hot water will tend all to go through there, especially if it is closest to the pump, it will circulate through the path of least resistance.
To cure this, close the lockshield valves fully, with the heating off, and wait until the rads go cold. Then open the lockshield on one of them by half a turn ONLY and feel if it gets warm when you start the pump. Only adjust it by a quarter turn at a time. You want the Flow pipe to be "too hot to hold" and the return pipe to be "too hot to hold for long" which is about 20C cooler. Adjust all the lockshields like that, then run it for a bit and see if the temperature drop between flow and return on all rads is still about right. Do not adjust any of them more than a quarter turn at a time while you are fine-tuning, and wait at least ten minutes before making another adjustment. You can hire or buy pipe thermometers or an infra-red sensor if you want to be any more accurate.
It is also possible that your system has a bypass pipe fitted to allow circulation even if all the rads are turned off, as might happen if you have TRVs on all rads and no room stat. In this case you will find the flow and return pipes at the boiler are both very hot, and all the rads are cold, so you have to follow the pipes until you find the bypass connecting hot and cold. It may have an adjusting valve on it but should never be fully closed.
After you have finished cleaning out your radiators, add a corrosion-preventing chemical such as Sentinel X100. As you have no tank to pour it in, you will have to add it into a pipe or a rad bleed orifice using a funnel or injecting it under pressure - there are tubes available that will fit on a skeleton gun such as is used for silicone sealant. It will be easier to get the chemical in when the rad is empty and the system is not pressurised.
