After upgrading to 10.4, it seems that you can't disable the "English" keyboard layout in the International System Preferences panel. This is very inconvenient for Logitech Keyboard users, because OS X seems to have its own mind about switching between "English" and "Logitech US/UK Intl" for input.
Until Apple or Logitech release a fix for this behaviour, you can remove the "English" keyboard layout by disabling (e.g. moving or renaming) the file named Roman.bundle in /System -> Library -> Keyboard Layouts. This should remove the "English" layout from the system, and allow you to use the Logitech Keyboard Layout as the sole input method.
[robg adds: I would strongly suggest renaming this file, not removing it, just in case. I prefer to never delete core parts of the OS, just in case something happens and you need the file again...]
Mac OS X Hints
http://hints.macworld.com/article.php?story=2005081214473681