isolate the cold water supply to the tank that feed the cylinder. Now open all you taps that are fed by the tank/cylinder until they are showing no more water.
Now theoretically your cylinder will still be full but there will be no pressure forcing the water out (cold water storage empty as supple isolated). There will be a little bit of water left just above where the hot water leaves the cylinder, how much depends on how well the system was installed. Slowly undo the immersion heater to test how much water is left in the pipe (at this point there may be a bit of water so I'd advise a bucket or a bin bag, one without holes!) and let it drain down.
Eventually the water should stop coming and you should be able to remove the immersion heater.
don't want to sound like an old man but here goes... please isolate the electrical supply to the immersion heater before you do anything else!
If that doesn't work then I don't know, that's how I changed one before!
Yes turn off cold water stop tap and then open hot tap on both basin and sink also tie up ball valve on header tank to stop header tank filling main tank back up. then you can take out immersion heater coil. when doing this dont forget to isolate electric supply for immersion heater