Born in Bristol, Grogan attended Bromley County School for Boys. He served as a Sunday School teacher at a Methodist church and, under the influence of his pacifist minister, Grogan registered as a conscientious objector during World War II. While serving in the non-combatant corps, he was befriended by numerous evangelical Christians. They, along with C.S. Lewis’s Beyond Personality, encouraged his conversion to evangelical faith in 1945. He entered into membership of Kensington Baptist Church.