Sounds like you need/want a powerflush.
I had LMS do this recently among other things. They basically drained the system, inserted a big magnetic filter device into the central heating return flow, refilled with water and cleaning additive, then ran the heating through each radiator, one at a time. Finally the system was drained again, the temporary filters removed, and then everything refilled and inhibitor added.
The temporary magnetic filter was then inspected and you could see lots of fluffy black stuff which had come out of the system, which was quite satifying.