Lovely scaly London water has a nasty habit of clogging up the shower head (as well as the bath, kettle, draining board, and probably my kidneys).
Ordinary white vinegar is brilliant at getting rid of the stuff though. I buy it from my local cash & carry, in an enormous bottle for £4.
For the shower head, I unscrew the head, put it in a plastic bag, put a rubber band around the bag, and then pour vinegar in the open end of the shower head:
Leave upright for an hour or so and you’re done! It can help to give the shower head a bit of a wipe before replacing it too.