Hello Graham,
I just tested and I am unable to reproduce your problem, mp4 and other video files play without any problem in lesson in different pages I tested (tested both as a teacher and as a student). So it must be something special to your website, or your permissions, ...
Thanks for checking. I embarked on producing a screencast to show the issue, but guess what, I couldn't reproduce it either. Not sure what the problem could have been, especially as I haven't changed any permissions and the site is 100% vanilla, but it seems to be working now.
