Which glue works best with wine bottle corks ?

I am preparing to construct wood framed wine cork boards, trivets etc. and want to use the best glue for both gluing the wine corks to each other as well as to a substrate of wood and or fabrics?

I would probably use waterproof wood glue for bonding corks to corks, and corks to wood. As far as corks to fabrics goes you may want to use a clear flexible fabric glue like fabritac.