Fitton was a painter, advertising and poster designer, draftsman and printmaker born in Oldham, Lancashire. Apprenticed at the age of fourteen to a calico designer in Manchester, he attended evening classes at the Manchester School of Art part-time while working the docks at night; here he got to know the painter LS Lowry.
In 1919 he moved to London and attended evening classes under A.S. Hartrick at the Central School of Arts and Crafts from 1925. In 1928 he married the artist Margaret Cook. They settled in Dulwich where Fitton was to remain and worked as an illustrator and poster designer.
The 1930's proved to be a very active period for Fitton; he exhibited at the Royal Academy, the New English Art Club and between 1932 and 1952 with the London Group. He was appointed art director for the C Vernon and Sons advertising agency and had his first one-man exhibition in 1933 at Arthur Tooth and Sons and in 1935 exhibited in the Graphic Art Exhibition in Moscow. He also began to teach lithography at the Central School.
Fittons father had been a trade union leader and was active in the labour movement, attitudes that left their mark on Fitton. He became a founding and active member of the AIA (Artist's International Association) and drew cartoons for the Daily Worker and the Left Review becoming known for his witty and adroit caricatures of political leaders such as Mosley, Churchill and Mussolini.
Other work over the years included posters for London Transport; illustrations for Lilliput and other magazines; wartime work for the ministry of Information and Ministry of Education; and a number of notable film posters. He served on the art panel of the Arts Council and in 1957 was a member of the Chantrey Bequest purchasing committee. Elected RA in 1954, became trustee for the British Museum in 1968-1975 and Honorary Surveyor of Dulwich College Picture Gallery in 1970-1982.
Fitton was a shrewd and perceptive observer of London life, of its cafes, markets and characters. His works reflect his draftsmanship, sense of design and wit and range from works influenced by Sickert to domestic interiors reflecting the Eusto