I am quite certain that it is not only the Universities with a Royal Charter, as both the University of Regina and University of Saskatchewan have God Save the Queen at the end of their ceremonies-as do some high schools here.
"God Save the Queen" has been traditionally sung at the end of events such as cinema, theatre, the end of a school day. O Canada was typically sung at the beginning. Sometime, likely in the 70s it became less fashionable to sing God Save the Queen-so it sort of dropped off, although there are some insitutions that don't have it.
I did note though, that there is not a portait of the Queen at our local university when I looked around today. I endevour to fix that.