Vinegar works great, fast and super easy! Just pour in distilled white vinegar (about 35p a bottle at Tesco, much cheaper in a big bottle from Booker- catering wholesale chain) to cover the limescale. Leave it sit about 30 minutes - no boiling necessary - boiling vinegar smells nasty! Then just a quick swish with a bottle brush inside, a double rinse with water and all clean, all done.
Of course the best way to avoid limescale (and to save energy) is to only boil the amount of water you need (fill tea cup from tap then pour into kettle) and tip out the kettle after you've filled your cup. If there isn't water standing in the kettle, it doesn't accumulate lime scale for ages.