Redman was born on 8 April 1910 in Rochester, Kent, England. His parents were Arthur, an officer in the Royal Engineers, and Vera Redman. He was educated at Wellington College, an independent school in Crowthorne, Berkshire. He studied electrical engineering at the University of London, graduating with a first class degree. He then joined Midland Electric Light and Power Company. As an apprentice, he converted domestic houses from gas to electric lighting.
Redman disliked his civilian career and left it to join the British Army. On 1 September 1934, he was commissioned into the Royal Army Ordnance Corps as a lieutenant (on probation). His commission and rank were confirmed on 1 May 1936. From 1936, he served in the Middle East.
He continued his Service in the Middle East following the start of World War II. He was promoted to captain on 1 September 1940, and to major on 13 July 1941. He was appointed Deputy Assistant Quartermaster General at Middle East Command. On 1 October 1942, he transferred to the Corps of Royal Electrical and Mechanical Engineers. In 1943, he was appointed Assistant Quartermaster General at the War Office.
On 9 September 1942, he was appointed Officer of the Order of the British Empire (OBE) 'in recognition of gallant and distinguished services in the Middle East during the period November 1941 to April 1942'. In the 1963 New Year Honours, he was appointed Companion of the Order of the Bath (CB).
In 1943, Redman married Penelope Kay. Together they had two children; Anne, born in 1944 and Jeremy, born in 1949.
On 1 August 1948, he was promoted to lieutenant colonel. In 1951, he was appointed Deputy Director of Mechanical Engineering for the I Corps based in Germany as part of the British Army of the Rhine. He served in the post for two years. He was promoted to colonel on 15 February 1953. In 1957, he was appointed Commandant of the REME training centre, and served in that post for two years. He attended the Imperial Defence College in 1959. He was promoted to brigadier on 1 January 1960. On 29 June 1960, he was appointed Director of Electrical and Mechanical Engineering, therefore becoming head of REME, and made a temporary major general. He was later promoted to major general, which was backdated to 29 June 1960. He relinquished the appointment of Director on 4 July 1963.
He served in the honorary position of Colonel Commandant of the Corps of Royal Electrical and Mechanical Engineers from 19 August 1963 to 19 August 1968.
