OK.
The problem you have is fairly common with an old, open vented system.
Almost certainly the cause is this:
The steel radiators suffer corrosion due to containing water, and a small amount of dissolved air. This results in tiny particles of iron oxide (black in this case). The particles accumulate into sediment, much of it settles in the bottom of radiators; some in the poiler; and some in the pipes. If the water is hard it can aggregate with limescale to form a hard blockage.
most likly you have got a blockage in the pipe that comes down from the small feed and expansion tank in the loft and joins the main pipes, usually near the pump. It will be a 15mm pipe.
As it has hardened, the plumber will probably have to cut out the blocked section of pipe, and replace with a new piece.
i strongly recommend you to ask for a Magnaclean or similar to be fitted, it will trap other circulating particles before they can gather into another blockage. I would also advise a chemical clean, which you can DIY at trivial cost. Otherwise, the plumber/engineer will probably recommend a Powerflush, which will cost hundreds of pounds.
Whatever you do, get the Magnaclean fitted, the sooner the better. It will cost around £100 plus fitting. Black iron oxide is called magnetite and is attracted to a magnet. There is a powerful magnet in the filter that traps is. Brown rust is hardly attracted at all. Central heating sediment is mostly black iron oxide.
If you can't get a plumber tomorrow, look for the drain cock and a hosepipe and I may be able to help you top it up. The pump will wear out if run dry.
@Lennybythewoodas