After reporting the nex 7.xx series was not working, Martin gave me temporary ftp access to a server to see what was happening. Turns out some of the default urls in the variables.php file used http rather than https, though SSL was turned on.
Simple fix, but quite significant, so rather than waiting for the next release I just updated the current 7.04 release with some relevant changes. (I also updated the release history). So if you are having problems getting 7.04 to work, please download and try again. This has likely been in place for at least a few releases.
Thanks Martin for your help with tracking this down!
Cheers
Dan
PS. Martin, I tried to reply directly to your personal email, but the domain was bouncing...