Born at Cleckheaton in Yorkshire's West Riding, where his father ran a worsted-spinning mill, Wadsworth studied machine draughtsmanship for a short time in Munich (1906-7) before going to Bradford School of Art, and then to the Slade (1910-1912). In the years before the First World War he was involved with the Vorticists, and was a founder member of the London Group in 1913. He served in the Royal Naval Volunteer Reserve during the war.
After he was invalided out in 1917 he worked on dazzle-camouflage for ships. In 1919, his first one-man exhibition of woodcuts and drawings was shown at the Adelphi Gallery, directed by Frank Rutter. His one-man show The Black Country was held at the Leicester Galleries the following year. Wadsworth left the London Group in 1919, and became a member of the NEAC in 1921. He travelled widely. His later paintings tend towards nautical subjects, with meticulously rendered objects of assorted kinds, grouped together in a surreal way. A contributor to the journal Abstraction-Creation, he was also a founder member of Unit 1 in 1933. He became an Associate of the Royal Academy in 1943.Wadsworth's The Black Country, and Cahier XIII, together with a letter from Wadsworth to Michael Sadler were purchased 1991