Nash was born in London, the younger son of lawyer William Harry Nash who served as recorder of Abingdon and Caroline Maude Jackson. His mother came from a family with a naval tradition; she was mentally unstable and died in a mental asylum in 1910. In 1901 the family moved to Iver Heath, Buckinghamshire. Nash was educated at Langley Place in Slough and afterwards at Wellington College, Berkshire. He particularly enjoyed botany, but was unsure which career path to take. At first he worked as a newspaper reporter for the Middlesex and Berkshire Gazette, in 1910. His brother became a student at the Slade School of Art the same year, and through his brother Paul, met Claughton Pellew and Dora Carrington.
John Nash had no formal art training, but was encouraged by his brother to develop his abilities as a draughtsman. His early work was in watercolour and included Biblical scenes, comic drawings and landscapes. A joint exhibition with Paul at the Dorien Leigh Gallery, London, in 1913 was successful, and John was invited to become a founder-member of the London Group in 1914. He was an important influence on the work of the artist Dora Carrington (with whom he was in love), and some of her works have been mistaken for his in the past.