Educated at Ascham St. Vincent's School, Cunninghame Graham joined the Royal Navy in 1905 when he entered RNC Osborne,. His tutors thought well of him and in 1907 he progressed to RNC Dartmouth where he continued to get good grades in everything except engineering. He completed his cadet training on HMS Cumberland and passed out as a midshipman in 1910. One of his first postings was to HMS Cochrane, which was one of the ships that escorted George V and Queen Mary to the Delhi Durbar of 1911. He was promoted to Sub-lieutenant in 1912 and at the beginning of 1914 he was appointed to HM Yacht Victoria and Albert on which his father had also served.
At the outbreak of World War I, all Royal Yachtsmen were transferred to two ships in the Grand Fleet, HMS Agincourt and HMS Erin. Cunninghame Graham served on HMS Agincourt and saw action at the Battle of Jutland in command of number 4 gun turret,. He specialised in signals and was promoted to Flag Lieutenant in 1917.
After the war, he held a number of brief appointments, including a period as tutor at HM Signal School, before being appointed, despite his lowly rank, to HMS Iron Duke in the Spring of 1922 as Fleet Signal Officer of the Mediterranean Fleet, under the command of Admiral Sir Osmond Brock C-in-C. He gained the rank of Lieutenant-Commander in 1924 just prior to his marriage to Patricia Hanbury, the sister-in-law of Herbert Fitzherbert, the Executive Officer of the Iron Duke and was made a Commander in 1928.
Cunninghame Graham had the unusual experience of attending all three staff colleges: Naval at Greenwich 1929-30; Army at Camberwell 1930-31; and Air Force at Andover 1934. Between 1931 and 1934, he served as Executive Officer on the cruiser HMS Cardiff on the South Africa station . He was appointed Staff Officer (Operations and Intelligence) at Nore Command in 1935. Having resigned himself, as had happened to his father, to remain a Commander for the rest of his naval service, he was promoted to Captain, at the last possible juncture under the batch system then in force, on 31 December 1935.
In January, 1936, George V died and Cunninghame Graham, awaiting his first command, acted as Aide-de-camp to Prince Paul of Greece during his visit to London for the state funeral. He was appointed in the autumn of 1936 to HMS Tarantula as Senior Naval Officer on the West River in China. This was the time of the Second Sino-Japanese War. On his return from China, he was offered the post of Captain of the "stone frigate" HMS President, which he declined, going on Half-pay at his own request from 14 April 1938 until 2 March 1939, when he was appointed Captain of HM Signal School.
During World War II he held four commands. When war was declared he was serving as Captain of HM Signal School, which also entailed being Deputy to the Commodore of Royal Naval Barracks, Portsmouth, and, thus, oversaw the research into the development of naval RDF.
His next appointment, in 1941, was as Captain of the cruiser HMS Kent on the Russian convoys. HMS Kent was selected to carry a diplomatic party which included: H.E. Ivan M Maisky, the Soviet Ambassador; Rt Hon Anthony Eden, Secretary of State for Foreign Affairs; Sir Alexander Cadogan, Permanent Under-Secretary at the Foreign Office; and Lieutenant General Sir Archibald Nye, VCIGS, to Murmansk from where they would travel by train to Moscow for talks with Stalin. As the diplomatic party were without any ciphering staff, it fell to Cunninghame Graham to inform the Foreign Secretary that the UK had declared war on Japan. In the Autumn of 1942, he became Flag-Captain to Rear-Admiral Louis ‘’Turtle’’ Hamilton who had chosen to hoist his flag in HMS ‘’Kent’’.
Subsequently, in August, 1943, he was promoted to Commodore (2nd Class) in charge of the Royal Naval Barracks, Chatham, in command of 20,000 officers, men and women with a daily turnover of 1,000. Also during this time, he was an Aide-de-Camp to the King (his father had been a Groom-in-Waiting to Edward VII and an Equerry to George V) and was awarded a CBE in the 1944 New Year's Honours List. Finally in January, 1945, there came a second promotion to Rear-Admiral in command of the 10th Cruiser Squadron, and 2nd in Command of the Home Fleet, hoisting his flag first in HMS ’’Diadem’’ and then in HMS ’’Birmingham.
After the War he continued to command the 10th Cruiser Squadron (later 2nd Cruiser Squadron with his flag in HMS Superb), during which time, he took part in the victory celebrations in the Netherlands and had the honour of having Princess Juliana and Prince Bernhardt as dinner guests; he was also dispatched to Sweden on an official goodwill visit, being granted a private audience with King Gustav V.
In 1947, he became Admiral Superintendent at HM Dockyard, Rosyth., receiving a CB, and was promoted to Vice Admiral a year later. He was appointed Flag Officer, Scotland in 1950. He was advanced to KBE in the 1951 New Year Honours and retired in October of the same year. He received his final promotion to Admiral on 15 March 1952.
In retirement he became Lord Lieutenant of Dunbartonshire (1955–1968) and Keeper of Dumbarton Castle (1955–1981), the first Naval Officer to hold the post. In 1985, his widow donated his uniform and medals to the castle where they are on public display. He also was a member of the Royal Company of Archers achieving a final rank of Captain.
He donated his papers (1913–1980) to Churchill College, Cambridge and his naval archive (covering the 18th, 19th & 20th centuries)to the University of California, Irvine.
Born in Chelsea, Angus was the second child and only son of Commander Charles Elphinstone-Fleeming Cunninghame Graham MVO RN and Mildred Emily Barbara, daughter of Charles Walter Bagot, Rector of Castle Rising, Norfolk. He was baptised on 25 March 1893 in Holy Trinity, Chelsea, having Albert Edward, Prince of Wales (later Edward VII) as his godfather and Princess Louise, Duchess of Fife (later the Princess Royal), as his godmother. This led to his attending the coronation of Edward VII as page to the Duke of Fife, for which he was awarded the 1902 Coronation Medal.
In October, 1924, he married Mary Patricia, the youngest daughter of the banker, Col Lionel Hanbury of Hitcham House CMG, VD High Sheriff of the County of London (1920–21); they had one son, Robert Elphinstone, who followed his father into the Royal Navy; and one daughter, Jean, who first married Charles Jauncey of Tullichettle and secondly Harry Polwarth. He had seven grandchildren. He was the only nephew of Robert Bontine Cunninghame Graham, the Scottish author and politician, to whom he was heir.