Hi JBurnard,
You are correct that this setting is located under Host->Host Settings. Once you get there, look under Advanced Settings->Other Settings->File Upload Extensions.
However, based on your description, it is clear that you aren't logged in as a host user. DNN has two levels of "administrators" -- admin accounts and host accounts. Admins administrate a single portal, while hosts administrate the entire DNN installation.
Your first step will to be to get the host account information and log in using those credentials. If you are not able to do so, let me know and I can guide you to make the change directly in the database.
Hope this gets you started!
Brandon