Radcliffe was educated at Haileybury College. He was conscripted in World War I but his poor eyesight limited the options for service so he was allocated to the Labour Corps. After the War, he attended New College, Oxford as a scholar, and took a first in literae humaniores in 1921. In 1922 he was elected to a prize fellowship at All Souls College, Oxford. He won the Eldon Law Scholarship in 1923.
