Ackroyd attended Leeds College of Art from 1957–61 and the Royal College of Art, London from 1961–64, where he studied under Julian Trevelyan. Subsequently he lived for several years in the United States. He was elected to the Royal Academy of Art in 1988 and appointed Professor of Etching, University of the Arts, in 1994. He was elected Senior Fellow of the Royal College of Art in 2000, and in 2007 was made CBE for services to Engraving and Printing.

Ackroyd's works from the 1960s show his interest in both Pop Art, particularly artist Jasper Johns, and Minimalism. His complex compositions from that period often integrate pre-existing imagery such as newspaper clippings.

In the 1980s Ackroyd emerged as a landscape artist. Central Saint Martins College of Art and Design mounted a retrospective exhibition of these works in 2006 and kept an archive of his work. His works range from minimalist, nearly abstract impressions, to detailed images. Hhis work almost never includes the human figure, the landscape subjects are often of old human habitation. Hhis prints range from tiny etchings intended to be bound into books to huge etchings. His preferred medium for working directly on paper is watercolour, including a recent project pairing his watercolors with poems by Kevin Crossley-Holland, published under the title Moored Man. He has also designed a number of large-scale, etched reliefs in steel or bronze commissioned for architectural projects in London, Moscow, Birmingham, and Glasgow. Recently completed projects include a mural at the Sainsbury Laboratory at Cambridge University, showing scenes from the Galapagos, and a door at Great Portland Estates in London, W1. See also The Stratton Street Series, Categorical Books, London, 2003 (introduction by Ian Ritchie).