the other thing you could try is adding a chemical cleaner, such as
Sentinel X400, which will cost you about £15, and circulating it for 2-4 weeks. Bale out all the mud from the loft tank, and sponge it clean, BEFORE you start. It is not as good as a powerflush, but it will loosen sludge, and your magnetic filter will catch what it loosens and circulates. After a couple of days to start shifting the loose stuff, you can turn off all the radiators but one, open its lockshield ffully, and let all the flow go through first one rad, then a second, them a third, and so on, until it has gone through every one of them at full flow, then adjust the lockshields back and just run as normal for a few weeks. I'd want to look in the filter to clean it out and see how much it collects (scrape it into a jamjar, there will be a lot a first, then it will reduce as the sediment gets captured.
At the end of the 4 weeks you ought to drain and rinse the system, and refill with a corrosion inhibitor such as X100.
This is a fairly simple DIY job, and not expensive if you can find the time yourself to bleed the radiators, bale out the mud from the loft tank, and operate the drain cock.
It might take you a couple of hours each time so a professional would do a powerflush and charge you hundreds of pounds, but the DIY method is worth a try, costs little, may make an improvement, and will not make it any worse. He was probably hoping to save you expense. But without adding a cleaner, most of the the sludge and sediment will lie where it is.
For a better job, in summer you can take all the rads off and carry them into the garden to blast through with a garden hose, after using the cleaner to loosen it. The sediment is black and will leave a permanent stain on carpets and floors. Turn the rad upside down as soon as you get it off the wall. It is not toxic, just iron oxide.