Hall was born in Newcastle, England, the eldest son of the vicar of a working-class parish. At the outbreak of World War I he enlisted in the infantry and spent nearly the whole war in France (1914-1919), rising to the rank of major and receiving the Military Cross. He returned to Brasenose College, Oxford, for an abbreviated university education and one term at Cuddesdon Theological College.
He soon emerged as an energetic and articulate leader of the British Student Christian Movement and was appointed to the national staff in 1920. As missionary secretary he was a delegate to the World's Student Christian Federation conference in Peking in 1922. He formed deep friendships with a group of young Chinese Christian leaders, including the student evangelist T. Z. Koo and the YMCA leader, Y. T. Wu. From then on he attempted to understand and interpret Chinese politics from the Chinese point of view. His experience in the war and in the industrial north of England also led him to give priority to the needs of ordinary people, especially the victims of social upheaval. Later, as bishop of Hong Kong (1932-1966), he was criticized for his advocacy of the poor and his support for the Chinese revolution.
Ordination (1921), marriage (1922), a return visit to China on a peacemaking mission (1925-1926), and some experience as a parish priest in Newcastle (1926-1932) preceded his appointment to Hong Kong. The diocese then included most of south China and was about to be engulfed by the Sino-Japanese War and the civil war that followed. "R. O." brought to these turbulent years vigorous and creative leadership and an extraordinary ability to recruit able people, both Chinese and foreign, to assist him. Something of his spirit was captured in The Art of the Missionary, a book he wrote in 1940 that became a classic. (It was reprinted in the United States as A Missionary Artist Looks at His Task). The capture of Hong Kong and Canton by the Japanese left the diocese divided by battle lines. Hall moved to Kunming and assigned responsibility for continuing the church's work on both sides of the lines to Chinese assistant bishops. In 1944, in order to provide pastoral care for an isolated congregation, he ordained the first woman priest in the Anglican Communion, Li Tim-oi, an action at first repudiated, but years later confirmed by both Chinese and Church of England authorities. The reconstruction of the church in Hong Kong after World War II included establishment of thirty new churches, sixty-five schools, what became the Chinese University of Hong Kong, and a host of welfare agencies to deal with the needs of refugees and a rapidly growing industrial population. In 1966 he and his wife retired to Lewknor, their home near Oxford, where they lived until his death.