Coldstream was born at the Doctor's House, West Street, Belford, though the family moved to London when he was two years old. Coldstream became a soberly realistic painter and worked for some time in the 1930s with the pioneering GPO Film Unit run by John Grierson. He edited Coal Face with lyrics by W.H. Auden and music by Benjamin Britten. Auden (whom others found a trying guest) lived for some time with the easy-going Coldstream and his wife. Coldstream helped to found the influential Euston Road School in 1937, and from 1949, he was Slade professor at University College London for 26 years.
As well as being a fine painter, Coldstream was a gifted administrator. In particular he helped to reshape British art education, especially through his work on the national advisory committee (1958-71), which produced two 'Coldstream' reports.