Atkinson was born in Leamington. In 1967 he began to teach art at the Coventry School of Art while producing conceptual works, sometimes in collaboration with Michael Baldwin. In 1968 they, together with Harold Hurrell and David Bainbridge who also taught at Coventry, formed Art & Language, a group whose influence on other artists both in Britain and in the United States is widely acknowledged.
Atkinson stopped teaching at Coventry in 1973 and the following year left Art & Language. He has since exhibited under his own name, including at the 1984 Venice Biennale. In 1985 he was nominated for the Turner Prize.
As of 2003, Atkinson teaches art at the University of Leeds.