Hello Andrew Jayne,
Commenting cannot be turned off, per se, in a Forum. What you can do is "Lock" the Channel. To do that:
1. Go to the Forum Channel
2. Click the Actions Button (https://customercare.igloosoftware.com/support/knowledgebase/all_articles/articles/action_button )
3. Select "Lock". This will lock any future topics posted on that Forum.
4. You will then get a prompt asking if you also want to lock all posts, as well:
If you select "yes", that will also lock the replies on each topic within the Channel. If you select "no", people will still be able to reply to each topic.
Please let me know if this helps or if you have any further questions.