[Arran]

 Unless it is really coming apart I would try using a hypodermic needle with some yellow carpenter's glue and inject it into the cracks. I have a feeling that the reason why the gap won't close is a slight amount of warpage, but some good clamps will fit that, make sure you clamp the side you are not gluing as well so you don't accidentally pop it loose by clamping the other side. For the loose veneer on the inside or elsewhere you will probably have to use some blocks to clamp it down evenly, I would just wrap some chunks of plywood in saran wrap or stick them in a plastic bag so the block doesn't get glued to the veneer. Don't use Gorilla glue, if you mess up with Gorilla glue it's polyurethane so it's especially nasty to fix, yellow glue is water soluble so if you screw up you can clean it out easily.
Regards
Arran