Atkinson was promoted to the Court of Appeal in 1968, serving as a Lord Justice of Appeal until he resigned on medical grounds in 1971. He sat on the Court of Appeal panels that heard the appeal of James Hanratty in 1962, the appeals of the Great Train Robbers in 1964, and the appeal in 1971 in "Knuller, Knuller v DPP", a case of conspiracy to corrupt public morals in relation to gay contact advertisements published in "IT" magazine.