descaler fluid

Furnox DS-3 (sulphamic acid) is designed for the purpose. It's not suitable for use on some plastics, so I would try to separate the heater from any of the plastic shower bits first.

You can get it mail order (BES is good for the large tub - that's much more than you'll need for just a shower, but I slowly use it up descaling other things). Builder's/Plumber's merchants seem to stock just the smaller tub. B&Q used to keep it, but it probably got moved out to make way for the cushions.

Another vote for DS-3. You can often sometimes find a 2.5kg oval tub in the sheds. (note that will make over 100 gallons of descaler - so should keep you going for a bit!)