Marsh was educated at Westminster School and at Trinity College, Cambridge. He spent much of life working as Winston Churchill's right hand but he was also private secretary to a number of top government officials.
Marsh was also a keen collector and patron of the arts. He first specialised in the English watercolours focusing mainly on the works of Thomas Girtin (1775 - 1802), Paul Sandby (1731 - 1809) and John Sell Cotman (1782 - 1842) among others. He purchased Herbert Horne's (1864 - 1916) collection of British works on paper including an important group of Alexander Cozens. He soon became a patron of contemporary British painting supporting artists such as Mark Gertler (1891 - 1939), Paul Nash (1889 - 1946) and Stanley Spencer (1891 - 1959) which in turn became a valuable collection of art.
Marsh was appointed Knight Commander of the Royal Victorian Order (KCVO) in 1937 for his work in the civil service. He served on the committee of the Contemporary Art Society where he was chairman between 1936 - 1952 and he was made a trustee of the Tate Gallery.