You've run into ownership issues. I'm not sure, but I think if you elevate your privileges to root you will overcome the copy problem (see below). I realise you are doing it this way for speed of transfer, but you wouldn't have run into these problems if you had simply connected the backup drive to the HDR-FOX by USB and used the CF to do the transfer.
If I change permissions, is this temporary or permanent? Will that change the owner and therefore upset access for the humax when it's plugged back in?
I'm pretty sure the Humax configuration takes no notice of ownership. The Humax app (settop) runs as root.
With regard to root privileges, recent Ubuntus (and Ubuntu-derived Linuxes) have made it very difficult (if not impossible) to log in as root (for security). A "root" user is essentially a user with admin privileges rather than root privileges, and you can temporarily elevate privileges to root.
It's easiest on the command line, and executing graphical apps with root privilege is a bit of a lottery because they might not have been built to ensure ownerships don't go awry.
On the command line:
> sudo <command>
executes that command with root privilege, and you will be prompted for the admin password if sudo has not been used in that session within the last few minutes.
> sudo -i
can be run on a line on its own to give all subsequent commands root privilege until "exit".
("sudo" = Super User DO)
Having obtained root privilege, there are various switches for the cp command which will copy preserving ownership (look it up).
Graphically, I'm not familiar with Ubuntu, but I think you might be able to use the file manager to open a drive or folder with root access by right-clicking and selecting "open as root".