The following are organisations we have heard of that may accept donations of sheet music - please let MM know if any of this information is out of date.
Your local music library
Community and Youth Music Library: http://www.cymlibrary.org.uk/
West Sussex Music – accept donations of musical instruments and sheet music: https://www.westsussexmusic.co.uk/page.cfm?title=make-a-donation
Book Harvest – part of Bookaid - will collect: http://www.bookharvest.co.uk/
Oxfam – if all else fails! http://www.oxfam.org.uk/donate/donate-goods/what-you-can-donate