The adventures with vinegar continue Chez Bray but this is something that I have been doing for years! A really common question that lands in my inbox is how best to descale a kettle. So here is my go-to method:
Last thing at night when no one will need the kettle fill it with half white vinegar and half water.
Unplug it and move it away from its normal spot, put a little reminder on it to make sure no one boils the vinegar solution in the middle of the night and attempts to make a cup of tea with it!
Leave to soak over night and in the morning rinse it out REALLY REALLY well. You might also want to do a dummy boil of clean water to thoroughly ensure that any trace of vinegar is removed.