Many (all?) private schools are charities, the National Trust is a charity, my local area has a Carers Centre to support carers and that is a charity.
However I do think some are a bit of a con. My mother used to get lots of letters from animal charities. One was a donkey sanctuary in Devon that only had about 25 donkeys.
She used to get letters from them on a regular basis, very professionally printed, but by giving money you were in effect paying for the couple who ran it to live in a nice house in Devon with a couple of fields next to it with a few donkeys in it.
Very suspect !