Allen was born in Wellington in 1922. In 1945, after serving in the Second World War, he undertook art studies at Perugia University and Instituto d’Arte Florence, Italy. In 1948 he gained a Diploma of Fine Arts from University of Canterbury and in 1951 he became an Associate of the Royal College of Art, London. From 1953 to 1959 he worked in the New Zealand Department of Education as Field Officer to the Northern Māori Experimental Art Project, followed by a position as Liaison Organiser to secondary schools. He then joined the staff at the Elam School of Fine Arts, Auckland, where his transformation of the sculpture department occupies an almost legendary place in the history of contemporary art in New Zealand. In 1977-1987 he became Founding Head, School of Art, Sydney College of the Arts, University of Sydney.

In 1976 he was among the early exhibitors at the Experimental Art Foundation in Adelaide, South Australia. Since 2000, Allen re-staged a number of early works, such as the three-part Contact, (1974), the two-part O-AR (1974), Poetry for Chainsaws (1976), News (1976), Planting a Native (1976), in Adelaide, Sydney, Auckland, New Plymouth and Wellington. More recent video works have been shown widely in America, Germany, France, Netherlands and Auckland.

Allen's work had a significant influence on the development of post-object practices in New Zealand. His environmental sculptures place the experiential elements of spectatorship foremost, and his performances emphasised ephemeral process over and above the physical object. Allen’s work is included in collections in countries all over the world, including the UK, America, Australia, Japan and New Zealand.