Messaging can be turned off globally within the Administration > Module Management > Enable/Disable Modules, where it can be disabled completely or for individual sections of Ultranet.
To turn the messaging off only for students, the messaging needs to be turned ON for all the areas within Ultranet in the Module Management section (see above).
Once this has been done go to Administration > Group Admin.
Select the group you wish to disable messaging for (all students are placed into Year groups, so by typing 'year' into the search box and searching you will be able to select groups that contain all the students).
Click on the desired group to view its details. In the subsequent window, select 'Disable' in Messaging Inbox area.
To disable messaging for all students, repeat this process for all year groups.