He was born in Luton and attended the Margate School of Art, where he studied textile design. After school, he served in the National Service (and later lived) in New Zealand, Malaysia, and the surrounding area from 1954 to 1962. In Auckland, New Zealand, he met his future wife, Maudie McKinnon. Soon after the couple married, they settled in Glenfield, New Zealand. It was in New Zealand that Blackburn started painting; he would paint in the garden, having become accustomed to the weather, but then later moved on to the North Shore. His paintings were exhibited at the Circle Gallery in Auckland, which established him as a "radical" painter, with his "simple, reduced strong forms in limited pure, unmixed colours."
In 1962, Blackburn, with his wife and three children, returned to Britain, where the influential art collector and gallery owner Jim Ede saw his one-man show in London's Woodstock Gallery. Impressed by what he saw, Ede offered Blackburn a place in his Kettle's Yard gallery in Cambridge among artists including Peter Lanyon, William Scott, and Roger Hilton.
Soon after, Blackburn's ten-year-old daughter became ill and needed a kidney transplant. Blackburn volunteered, spending six months in intense physical training to prepare for the organ transplantation. The time spent before and after the successful surgery prompted Blackburn to drop from the public eye for a number of years.
In 2006, Blackburn had a show at the Metropole Galleries in Folkestone; his work had not appeared in a commercial gallery since 1968. This led to a revival of interest in Blackburn's body of work as he approached eighty-years old.
Blackburn's abstract paintings are held in the private collections of Paul Zuckerman and Natalia Grosvenor, Duchess of Westminster. In addition, his paintings are housed in university collections across Britain, including Cambridge, Kent, Essex, Newcastle, and Dublin. In 2008, he returned to Auckland for a show at the ARTIS Gallery entitled The Muriwai Paintings; this was followed by a show at the Osborne Samuel Gallery and Lemon Street Gallery in London in 2011. A 2012 show entitled And God cryed at the Studio 3 Gallery in Kent was a critical success.
Blackburn incorporates found objects and materials on his canvases, citing their "previous existence". His paintings utilize acrylic paint, oil paint, and encaustic, as well as resin, grit, house-paint, and varnish; according to a review of his 2015 show at the ARTIS Gallery, recent work "rides roughshod over any conventions of neatness and grace, using bold form, often black, and adorning his surface with found objects and collage." Of his own work, the artist says, "I suppose, that’s what my painting’s about; life itself is terribly dangerous, terribly cruel, terribly rewarding. All these things at once. This multi-faceted, wonderful jewel – which we all live with and die with – is there. We’re saddled with it, like it or not."