In 1945, Murphy commenced studying law at the Sydney Law School of the University of Sydney and, in 1949, graduated with a Bachelor of Laws with Honours. While at the University of Sydney, during both his science and law degrees, Murphy was politically and socially active and was involved in the Students' Chemistry Society, the Junior Science Association, and the Science Association. In 1944, in his third year of his science degree, Murphy was elected to the Students' Representative Council but was dismissed two hours after his election victory, on a "constitutional technicality". This event is said to have cemented his interest in politics and law, and he commenced participating in the university's debating society and its monthly debates the following year.