Cuneo was born in London, the son of Cyrus Cincinato Cuneo and Nell Marion Tenison, artists who met while studying with Whistler in Paris. Terence Cuneo studied at the Chelsea Polytechnic and the Slade School of Art, before working as an illustrator for magazines, books and periodicals. In 1936 he started working in oils, continuing with his illustration work. During World War II he served as a sapper but also worked for the War Artists Advisory Committee, providing illustrations of aircraft factories and wartime events.
After the war, Cuneo was commissioned to produce a series of works illustrating railways, bridges and locomotives. A significant point in his career was his appointment as official artist for the Coronation of Elizabeth II, which brought his name before the public world-wide. He received more commissions from industry, which included depicting manufacturing, mineral extraction and road building, including the M1. He was most famous for his passion for engineering subjects, particularly locomotives and the railway as a whole. But in fact Cuneo painted over a wide range, from big game in Africa to landscapes. Further success was achieved in his regimental commissions, battle scenes and incidents as well as portraits (including H.M. the Queen, and Field Marshal Montgomery).Revered by many of his peers and well-liked by the public, Cuneo was awarded the OBE and was a CVO. A 1.5 times life size bronze memorial statue of Cuneo, by Philip Jackson, stands in the main concourse at Waterloo Station in London. It was commissioned by the Terence Cuneo Memorial Trust (established March 2002) to create a permanent memorial to the artist, together with an annual prize at the Slade School of Art, given by the Trust. In tribute to Cuneo's trademark, the statue includes a hidden mouse peering from under a book by the artist's feet, and another carved into the statue's plinth near the ground.