John Purcell Paper is a good place to buy paper and greyboard. They are based in Brixton and if you visit them in person you can pick up some free paper samples. You can also ask for samples over the phone. They specialise in printmaking papers.
GF Smith also sell paper, including a range of papers for digital print.
Ratchford sells a great range of bookcloths and lots of other bookbinding materials and tools.
Shepherds Falkiners have a shop near Victoria station. They specialise in tools and materials for bookbinding as well as some very nice papers that are suitable for bookbinding and printmaking.
You can buy things like bodkins, spring dividers and pin vices (0-1mm) in tool shops. Before you invest in an expensive bookbinding brush you might consider buying a paste brush from a decorators shop as they are much cheaper.