Parazone Bleach Blocks
(not bloo, not yellow, not scented, not Harpic)
They will gradually loosen and dissolve the lime scale. If you look inside after a few weeks you will see the float starting to come clean, then the scale will flake off the sides. Eventually it will all be gone. Put a new block in about once a month.
Better still, it will clean out the scale from the waterways or holes that feed flushing water round the rim, so the flush improves, and the will reduce the scaling in the pan, so it is smoother and stays cleaner.
If the water supply to the ballcock comes in through the bottom of the cistern (stupid design but looks neater) instead of the side, cleaning away the scale coating may make the rubber washer at the bottom start to leak if it is 20 years old. Keep an eye on it and replace if necessary. It will start with the tiniest drip.