I would suggest that 2 great places to start to enquire would be the Students Union- Students could get involved with RAG (Raise and Give) or look to offer help and support to societies who wish to put on events.
Secondly another great place to try would be the Sports Department- They’re always looking to promote fixtures or increase their participation in sport rates- Putting on events is a quick win to get the masses involved!
Of course their are always restrictions- Universities won’t want anything which is a potential conflict or interest or damaging to the student experience or reputation of the university, however on the whole universities are very receptive to students wishing to gain experience.