if you like simple plumbing. take it off, empty it into a bucket, turn it upside down, carry it into the garden and wash it through with a hosepipe. That is a good way of getting a single rad clean.
While the rad is off, turn on the rad valves one at a time to squirt into a bucket and see what flow you get, and if sludge comes out
Bale out the F&E tank and sponge it clean to remove the mud
For only £15 you can buy a litre of Sentinel X400 which will soften existing sludge and let it wash round on the pump, run it for about 4 weeks before draining it out and rinsing it, this is a cheap and fairly easy DIY way to get a lot of loose sediment out. It will not clear a blocked pipe though if there is absolutely no circulation for the chemical to travel through it. As it is summer now, you can run the pump with the boiler turned down to save energy. If you close the rad valves, and open one of them at a time, full, at each end, it will give a better flow through that rad to loosen the sludge. I assume you do not have a combi so turn the pump speed to high (look at the F&E tank to check it is not pumping over)
If you can afford £100 and fit a Magnaclean, I guarantee you will be amazed and delighted to see how much black sediment it traps out of the water. plumbing it in is fairly easy while the system is drained.
I am a householder not a pro but have done all this.
Tapping the rad with a rubber mallet during flushing is supposed to loosen sediment and help it be washed away. Not everyone approves of it. If you have X400 in the water and preferably a Magnaclean fitted, I expect those bits will wash away and get trapped. Otherwise, you would not want them to float around and get stuck in the pump or anywhere