Danfoss is a major and good quality manufacturer, and may still be able to supply replacement heads (if needed) to fit your old valves.
hot across the top, cools when turned down
may be badly sludged
heats all over, cools when turned down
correct behaviour
hot across the bottom, cools when turned down
is full of air, or badly sludged.
warm extreme bottom right, cold elsewhere.
insufficient flow. Turn off ALL the others and see what happens. May improve if all rads are balanced
right becomes hotter when other radiators are turned off and there is some heat across the bottom, but the top stays cold
air, or sludge, also poor flow
hot across the bottom, no noticeable change when other radiators are turned down
Air or sludge
hot all over, cools when turned down
Correct
So it seems to me that you have a sludge problem. The air you can easily bleed out, and the balancing can be addressed later.
I would recommend starting with a simple chemical clean. If you are fond of DIY plumbing it need only cost £20 for chemicals, plus two half-days of tinkering. You will need to find a downstairs drain cock, and (probably) a small feed and expansion tank in the loft. Or a plumber or heating engineer can do it. You do not need to pay Gas Engineer prices because it is not gas work.
If you are fond of plumbing and strong, you can also take the rads into the garden and squirt a hosepipe through them.
I would also recommend fitting a magnetic system filter, to capture loosened sediment, on the Return pipe to the boiler. It is not a difficult plumbing job. Preferably fit it before doing the clean as it will stop sludge moving into the boiler.
A chemical clean is not very intensive, but it will certainly do nothing but good. If more work is needed afterwards, it will not have made things worse.