Oxfam, Dorothy House Hospice, and Julian House. Dot House and Julian House are both local charities.
Many of the charities will pick up large (both in quantity and size) donations by request, but they also put these bags through people's doors. They're large bin (trash) bags, usually with the charity's name on. You then leave the full bags outside your house on the designated day ready to pick up. It's a system that works really well. You do have to be careful to check that you're giving to a charity as there are a few questionable companies around who give the impression of being charities, take you donations, and then sell your clothing at a premium rate abroad.