Atkinson was born in 1939 in Thurnscoe, near Barnsley, Yorkshire. 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 the UK and in the United States is widely acknowledged.
Atkinson was founder-member (with colleagues John Bowstead, Roger Jeffs and Bernard Jennings) of the group Fine-Artz (1963), and (with David Bainbridge, Michael Baldwin and Harold Hurrell) of the group Art & Language (1968-74), two of the most influential collectives in contemporary Western art.
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.