Thanks for this... in my rapid and steep learning curve, I did end up thinking this is one of the places that I may need to make the change, although I had no idea where to create the files and what they should look like.
It appears that the problem was that the WHM environment was configured with a temporary setup, ready to take the migration from another cPanel configuration. The Hostname needed to be changed AFTER the migration had taken place. So there was some tweaking with modules and we also set the domain as a Remote Mail Exchanger, but this made no difference until we changed the Hostname.
Thanks for your reply, and at least you started on the right lines so I'm confident we would have got there should I not have found the culprit already!