I'm not quite sure if I've got this. Is the problem no water from the taps or are you getting water but its not hot/heated?
For the first, could be airlock or sludge/blockage. Try the old hose between the taps at the kitchen or connect the two w/m valves together and blow through for a few seconds. Make sure the valve next to the H/W Cylinder(the one in the airing cupboard) is not turned off.
If you are getting water from your taps but its not heated, check your boiler is working(are rads getting hot, can you see the pilot light/boiler firing up).
If the boiler is working check any thermostats.(Make sure its set to call for heat. Listen for a "click" as you change the setting.) There is commonly one strapped to the cylinder for hot water. If a thermostat is broken it will need replacing(usually inexpensive).
If all these checks leave you scratching your head, you might have sludge in the flow or return pipe to the cylinder or a broken diverter valve. If you know where your valves are(next to or near the boiler usually) check those for operation.
hope this gives you some ideas.
Quote:I think the lower part of the tank should be hot from the CH system, making the upper part of the tank (hot water) hot too. Have I got it?
Not quite, yes the heating water is seperate from the H/W but it's not "layered" in the cylinder. If you look at it you will see 4 main connections on the cylinder, one from the top, one very low on one side and two, one above the other on the other side(you may have others too) it is these two pipes that are your flow/return pipes from the heating system. The water flows in one pipe and out the other, but it doesnt really go "in" your cylinder. these two pipes are directly connected through a long coil of pipe wrapped inside the cylinder. Its this coil that heats your hot water. (the coil has a far higher surface area than your stratofying method, therefore more heat goes between it and the water to be heated.)
btk