What is the ruling on the presence of music in British educational videos for university students?

If you are in need of this study, there is no harm in you continuing it. You must fear Allah as much as you are able concerning the sounds of music. If it is possible for you to ask the teacher to lower its volume, then do so. If that is not possible, then you may plug your ears with something until the sound of the music ends, because what is forbidden is listening [intentional], not merely hearing [unintentional].