I used to help at the MS Therapy Centre Lothian: 40c Swanfield, Bonnington Road, Leith, Edinburgh EH6 5RX. At that time they collected used stamps to help with fundraising - it is funded almost entirely by donations. Thay had an arrangement with a local stamp shop to buy the stamps. It didn't make a vast amount, but every little helps.
Ther only problem was that if the stamps are packed loosely in the envelope, they all squish up to one end so that when it goes through the machine at the sorting office it comes up as a thick package and needs more postage - and they have to pay for this at their end as excess postage. It can be more than the stamps are worth.