The Sparrows' Nest opened in December 2008. They held a very interesting meeting at the London Anarchist Book Fair last October.
Information from http://thesparrowsnest.org.uk:
Online Catalogue: Online catalogue with searchable keywords: ANARCHIST BOOKS/PAMPHLETS - note this is a table of all content with fairly large file size (6MB) so wait to load before searching. Use search facility on your browser. Alternatively, Download/print catalogue ordered by author or by title (no keywords, around 700kB filesize). Last updated 19-April-2013.