Try a company called LMB their sorting facilities are based in east london and they have collection banks all over. I went to their sorting plant to collect some recycled fabric for a project I was doing. I definitely saw smaller pieces so am sure they will take yours if you contact them and find out the best way to do it.
I am trying to find a place in the US for my textile runoff as well! We re-use most scrap but Serger runoff etc is not something we can use.
We tried to find somewhere years ago and turned up nothing.
I saved my workroom non-recyclables for all of 2010 and it amounted to one large household garbage bag :) It was in a lovely vase at my table at the Elegantly Green Wedding Showcase.
Really not cool that thread spools aren't recyclable including Gutterman who I assumed would have it figured out by now.
Not sure if it's of interest, but we recently started an Offcuts & Reclaimed section to our site: http://bit.ly/f7FbGP
You could defo add them on there if you wanted?
I volunteer for a company charity called Fine Cell Work. They are always looking for fabric donations. Depending on whether it is relevant/what they are looking for, it might be worth contacting them through their website?