Death Goes To School (top right image) is a 1953 murder mystery at an all-girls school.
When one of the teachers is murdered, due to her abrasive relationship with the others there are a number of suspects.
The case is investigated by Inspector Campbell (Gordon Jackson) and he is helped by one of the teachers, Miss Shepherd (Barbara Murray).
The murderer is Miss Hopkinson (Beatrice Varley) who takes her own life before she is arrested.
Movie pages here.