Griffith graduated from the LSE LLB Programme with first class honours in 1940, his last year spent in Cambridge where it had moved as a precaution because of the war. Initially a conscientious objector, he later became an officer in the Indian army. On demobilisation he took up a position as a lecturer at the University of Aberystwyth, while working on an LSE LLM thesis. In 1948 he returned to the School as a lecturer. He would spend the remainder of his career at LSE, becoming professor of English law in 1959 and professor of public law in 1970. In his history of LSE, Dahrendorf describes Griffith as “the conscience of the school and the guardian of its tradition in critical times”.Griffith later recalled that as a student he regarded much of the discussion of public law as politics dressed up as legality. That was a theme which recurred in later writings, notably his famous book, The Politics of the Judiciary, in which he argued that the narrow and conservative background of judges in many ways explained their judgments. He opposed the incorporation of a Bill of Rights into UK law as conferring undesirable discretionary powers on judges. Griffith’s more scholarly writings ranged over local government, legislation, and parliament and culminated in a number of fine, empirical studies of Parliament and public administration.
In the 1950s Griffith served as a local government councillor. Over the years he was a regular contributor to the New Statesman and The Spectator. He was in the tradition of the radical English–Welsh dissenter. He enjoyed controversy. When in the 1980s the view of some was that speakers at universities should be denied a platform if they were thought to be racist or fascist, his view was that, save in a small number of cases, the free exchange of opinion was to be defended.