There is a better way: just boil 100-200g of citric acid in a kettleful of water. It will dissolve the limescale with no damage to the heating element.

You can also use vinegar to remove the calcium.

Yeah but it takes way longer if you need to remove a thick layer of calcium. What you can do is put in vinegar and then turn the kettle on. It improves the effectiveness of the vinegar, but it gets all frothy and stinks up your house. Also if you are are with your face over the kettle when you open it, the vinegar steam or whatever it's called stings in your eyes. So personally, my money is on turning the kettle on with no water :) (well actually my money is on buying a calcium filter, which is what I ended up doing in the end, but apart from that :) )

That will remove limescale from the heating element. Unfortunately some of it also finds its way into the auto-cutoff mechanism, causing it to switch off prematurely (or occasionally fail to switch off.)