Kendrew played rugby union for England 10 times and was captain of the team in 1935. He was a member of the 1930 British Lions tour of Australasia but did not represent the Lions in any of the test matches. He captained the Army Rugby Union team in the Army Navy Match against the Royal Navy winning 11–8, on 2 March 1935. In that match he played in a formidable front row of prop Frank Whitcombe and hooker A. J. A. Watson, in a famous victory with the Army team having only 13 players; for most of the match the scrum packed down with only six forwards due to injuries.
Kendrew was commissioned as a second lieutenant with the Leicestershire Regiment Supplementary Reserve of Officers on 18 January 1930,[4] and joined the regiment on 28 August 1931.[5] He was promoted to lieutenant in 1934, captain in 1939 and major in 1946 (he held appointments as acting or temporary major, lieutenant colonel, colonel and brigadier at various times and ended the war as a war substantive lieutenant colonel).[6] From November 1936 until December 1938 he served as assistant instructor and instructor at the Tank Driving and Maintenance School (subsequently the Armoured Fighting Vehicle School) at Bovington Camp. Kendrew was then an instructor at the Royal Military College, Sandhurst until 1 September 1939, two days before the Second World War began.[3]
After the war, from June until November 1946, Kendrew was general staff officer, 1st grade (GSO1) (Infantry) at Central Mediterranean Forces headquarters. Two training appointments followed immediately: until August 1948 he was commandant at the School of Infantry of the British Army of the Rhine and then commandant at the Army Apprentices School, Harrogate until 13 September 1950. Kendrew had been appointed several times as acting and temporary lieutenant colonel, colonel and brigadier from March 1943 and on 28 July 1951 he received the permanent rank of colonel.[7] He was appointed to the Adjutant General's and Quartermaster General's Staff, Northern Ireland District in October 1950 and served there until 27 September 1952.[3]
During the Korean War, as a temporary brigadier, Kendrew commanded the 29th Infantry Brigade, Commonwealth Division and received the rare distinction of a fourth award of the DSO. In 1954 and 1955 he served at the Imperial Defence College. He was Brigadier A/Q at the adjutant general's & Quartermaster General's Staff at Headquarters Northern Command (York) from 10 March 1955 until 28 September 1956.[3]
Kendrew was appointed in the temporary rank of major general as general officer commanding and director of operations Cyprus District in October 1956 until October 1958,[8][9] during a turbulent period of British rule. In September 1958 he survived an assassination attempt by EOKA fighters,[10] which killed one of his escorts.[11] During his time in Cyprus, Kendrew's permanent rank was advanced to brigadier on 19 April 1957,[12] and then to that of major general on 29 June.[3]
For two years from December 1958,[13][14] Kendrew was director of infantry at the War Office in London. He was the director of information at the War Office from 1959 to 1960 and then head of British Defence Liaison Staff at the British High Commission to Australia in Canberra from 1961[15] to 1963.[16] He retired from the army on 1 September 1963.[3][17]