old? Black and dirty water?
it will have lots of old sediment in it.
Taking off the old rads (they will dribble black sediment when you take then off until you turn then upside down to carry them into the garden) and squirting then through with a hose will do a lot to wash it out. While you have them off, turn each rad valve on and let it squirt into a bucket. As long as every valve will squirt, you know you have at least some flow (if not you have a blockage which is much worse)
Put the rads back and refill the system, adding a litre of sediment-loosening cleaner such as Sentinel X400 which will cost you £15 at the DIY shed or plumber's merchant. Run the system as normal for 4 weeks, you will find the water goes inky black quickly, this is with old sediment that the chemical has loosened and is now washing round in the water
Then drain and rinse it well, and add a litre of Corrosion Inhibitor such as Sentinel X100 on final fill;,. This will prevent future corrosion.
That lot will take you a couple of afternoons work and cost you about £30, and will do a lot of good and get you out of trouble for now.
If you can do basic DIY plumbing there are some other things you could do that will improve the system without a lot of work or making big changes:
You could add a Feed and Expansion Tank in the loft (if you have one) that will prevent you having to manually top up your strange wall tank
You could replace the old rad valves with new lockshields at one end, and thermostatic valves at the other (I am assuming your old rad valves are extremely old and are liable to jam or leak). It will be cheaper, but just as much work, to use manual valves rather than TRVs
You could add a magnclean on a 22mm Vertical pipe on the return to the boiler. This will trap circulating black particles before they can form future blockages (you can never get it all out) and it will continue working permanently. I guarantee you will be amazed and delighted to see how much sediment it traps. The device will cost you about £100 and might take you an hour to fit if you are a DIYer like me.
Old systems can work for a surprisingly long time with a bit of care, so this could save you a lot of money and put off the time when you need on a professional upgrade