Born in Maxwelton, Kirkcudbrightshire. His father, H. Sharpe Gordon, was a solicitor. Educated at Marlborough before entering the Army in the RFA; he was wounded and invalided out in 1918, receiving the Military Cross. After the war he entered Pembroke College, Cambridge, initially to study history but changing to natural sciences.
He won a scholarship to the medical school at St George's Hospital. After qualification he obtained the post of resident medical officer for one year, before studying dermatology and radiotherapy at St Louis Hospital in Paris, France and Vienna, Austria. On his return to London he was employed at St John's Hospital, Lewisham, the Shadwell Children's Hospital and the East Ham Memorial Hospital.
In 1933, he joined the staff at St George's Hospital as assistant skin physician, relinquishing his three previous appointments, but adding two others at the West London Hospital and the Cancer (now the Royal Marsden) Hospital in Fulham Road. His roles at St George's later also encompassed those of an administrator and acting dean of the medical school, as well as director of the V.D. (veneral diseases) department. He was responsible for the introduction of female students from Cambridge to St George's following the Second World War; while women had been allowed to study medicine at St George's during the First World War, they had not been admitted in the interwar period.
In 1939 Gordon was appointed sector dermatologist to the EMS Sector Seven which entailed weekly visits to a number of hospitals. At the Cancer Hospital he became an expert at treating the various skin malignancies, and his previous interest in radiotherapy proved valuable. He soon became intrigued by the possible role of hypnosis in the treatment of various skin conditions, and with the assistance of Kathryn Cohen (who had studied at St George's as one of the first female students in 1945 and was working at St George's Hospital as a psychoanalyst) and S. Mason, he undertook a study and presented the results to the 1952 International Congress in London.
In 1963 he was president of the British Association of Dermatologists, and also president of the dermatological section of the Royal Society of Medicine. He was chairman of the medical staff committee at St George's for three years and was Governor of St George's Hospital 1948-1952.
He was married to Jean Robertson; they were married at St George's, Hanover Square.