Welcome to Just Answer. I will do my best to fully answer your question(s).
The black color that appears is likely from a build up of deposites somewhere in your water piping system. This is usually temporary, harmless, and caused by a disruption in water pressure from a system shut down, maintenance, and re-start. Air entering the system from it being drained down can cause this to happen.
If you recently had some work done to your water system I recommend running the taps, both hot and cold for about 5-10 minutes to see if that clears it up.
If you have not had any work done then something else is going on, possibly the softner not working properly, or as you mentioned, the hot water loop pump not working properly.
For the latter situation I would have a plumber come out to see whats causing the black water. Just to be certain it is safe to use and drink.
We get minor water hammer everytime the washing machine runs, which is almost every day. I also topped up the pressure on the heating side of the water system about a week ago, only by a very small amount. The heating/boiler hot water and the hot water that comes out the taps are two separate circuits, so it shouldn't be those, unless there's a hole in the hot water cylinder connecting the two. Its an expensive Belgian tank-in-tank cylinder, so I can't imagine it would have corroded. If there was leakage between the heating circuit and the hot water coming out the taps then wouldn't you expect more of a continuous discoloration of the water?
I replenished the salt in the softener almost a week before the black water appeared....? This morning I tried to bypass the softener but it turns out that the bypass valve is defective and cannot be opened fully, so I can't isolate the softener until our plumber fits a new valve next week. I will try again then. There are no larger black pieces associated with the stained water so I'm not sure it is either mould or rubber which you might expect to produce a range of grain sizes rather than a homogeneous grey/black solution. We checked the small header (pressure maintenance??) tanks associated with the boiler and hot water cylinder to see if the bladder had gone in either of them, but they appear to be fine.
After isolating the softener to see if that makes any difference, my next step will be to get the boiler serviced - the plumber that does this may be able to shed a little more light on things.
I have been following your post since I opt-ed out to another expert. The next expert said basically the same thing but in different terms. BotXXXXX XXXXXne your doing exactly what I suggested you do. We both agree there is a form of something deposited in your system, where it is coming from is going to have to be determined from a service call to your location. The water hammer "may" be causing this turbidity to a degree but as I suggested, please get a plumber to check it out. It appears you are close to doing so. Better safe than sorry.