[Arran]

At first glance I thought that maybe the cabinet was water damaged, which would be a more normal reason as to why a top would come off, hence why I suggested trying to remove the sides for a repair. But it looks like the grilles in the front are pretty solid, something they would not be if the radio was water damaged. If there were room I would add a solid block from back to front, on the inside corner to support the top, then glue it and screw it into the side, then it will never come out.
Regards
Arran