Hospices are charities, having worked in one I know that they receive some annual funding from the NHS, but the great majority of their vital expenditure is funded by public donations, legacies etc.
The Lifeboats are another charity which I am amazed to find gets no central funding at all, again it all runs on charitable donations.
In answer to your question - I don't understand how institutions like Eton College get charitable status, when well-heeled parents pay for their boys to attend. I'd say that the majority of charities to do with health or old people or animals really need the money from us.