A radiator that is hot at the top and cold at the bottom is a common complaint, and it is routinely met with the same advice given for the opposite symptom: bleed it. That advice is wrong here, and understanding why makes the fix obvious.
Which end is cold tells you what is wrong
Cold at the top, warm at the bottom means air is trapped in the radiator. Air rises, sits at the top, and displaces water. Bleeding releases it and the problem is solved.
Cold at the bottom, warm at the top is the reverse situation and has a different cause: sludge. Corrosion products and debris settle by gravity and build a layer along the base, blocking circulation through the lower channels.
Bleeding a sludged radiator releases nothing, because there is no air in it.
Why it matters beyond one cold radiator
Sludge is not confined to the radiator you noticed. The same material circulates through the pipework, the pump and, in a combi system, the heat exchanger — which is a considerably more expensive component than a radiator.
A single cold-at-the-bottom radiator is usually the first visible symptom of a system-wide condition rather than an isolated fault.
The fixes, in order of cost
Removing and flushing the individual radiator outdoors with a hose is the cheapest option and often restores that radiator entirely.
A power flush treats the whole system and costs considerably more, but addresses the cause rather than one symptom.
Whichever is done, a corrosion inhibitor should go back into the system afterwards. Without it the same process simply begins again, and the radiator that was flushed this year is the one that goes cold in three.