If you have updated your wiikey to play a backup of super mario galaxy ( ie update 1.9g) , that update introduced a problem to the drive and it could not read original dual layer disks (backups worked as silly as it might be).
SSBB comes in a dual layer dvd so your wiikey will not be able to read it (if your last wiikey update was 1.9g).
that issue was addressed in the 1.9s wiikey update. You have to download the iso from
http://www.wiikey.cn/resources.html
(the pal version for your case i would assume) and boot your wii with that disk. it will perform the update. There is also a config disk you can download if you like.