Hi all.
Now, it will take greater minds than mine to explain this but

...having totally disabled User Account Control and still having the problem I became unconvinced the issue is anything to do with administrator level access but probably more something like Realband is stuck in a partial, unfinished rebuild of the Stylepicker.

After trying everything else I overwrote Realband 2016 with an installation of Realband 2015. (Just Realband, I left BIAB 2016 untouched). Hey presto, Realband 2015 did a longer rebuild on first opening and then worked fine.

I then upgraded again with a re-installation of Realband 2016 (making sure I installed always as the administrator) and...everything works fine.

User Account Control is still active but I'm running the program as an administrator.