hi it sounds like you have a primatic or an auto vent cyld and the seal has gone it will need replacing but primatics are few and far between to get nowdays, so it will need to be replaced with an indirect cyld with a coil internally and a seperate header tank,
Under the latest regulations its a reportable item to building control if you plan to do it yourself , but if you get a plumber registered with I O P or Corgi then they can self certificate you will notice on the side of the new one is a certification form to be filled in
Is your hot water heated solely by the immersion heater, or is this a back-up for your central heating boiler? I'm not sure what you mean by a "double copper tank". If the central heating boiler heats the water, it could be that the heating coil inside the hot water cylinder has sprung a leak, allowing water from the heating circuit to get into the hot water system. If that were the case it would be a new cylinder.
One way to check for this might be to see if the central heating top-up tank is drawing in fresh water. You could do this by tying up its ball valve for a day or two to see if the level drops in the tank. The top-up tank will be the smaller of the two cold water tanks at a higher level than your hot water tank, possibly in the loft. That's assuming that you have an indirect vented hot water system. Your description "black gunge" does suggest to me that it has come from the heating system.