If this is in small pieces then many school art departments will be happy to take it for collage.
Larger pieces can be wanted by schools as well or amateur dramatic societies. The very best fabric locust I ever came across was a fashion student who was very pleased with many of my less sensible fabric false economies! (they were all such a good idea at the time when I bought them!)
The quickest way of disposing creatively of fabric in large quantities, pretty much regardless of the size of pieces or nature of the fabric is the Scrap Store.
Here is the link to the website for the one in Bristol. It includes information about the many items they are happy to receive as donations and a list of other scrap stores about the UK. My local one is Swindon Children's Scrapstore and they make excellent use of their donations, helping other voluntary groups as well as schools.