A wooden casket is fine for transporting the Ashes into the uk. You will need a copy of the death certificate, a copy of the cremation certificate and a declaration of contents letter which can be issued by the funeral home in the US.
there no reporting requirements for the ashes entering the UK, you will need the cremation certificte for any formal disposal of the ashes in the UK (burial in a cemetery etc).
Good luck, if you need any further information please feel free to PM me.
Stuart
(a UK funeral director)