Holden was born in Manchester in 1919. He studied agriculture and veterinary science before meeting David Bomberg at the City Literary Institute in 1944. Along with Dorothy Mead and Edna Mann, Cliff Holden followed Bomberg to the Borough Polytechnic and studied with him from 1945 to 1951. In 1946, Holden was a founder member the Borough Group and was president of the Group between 1946-48. He was the author of the Group's manifestos. By this time Holden was romantically involved with Dorothy Mead, and the two travelled to Spain and then onto Sweden together. Although Mead returned to Britain in 1956, Holden remained in Sweden and lives there to this day.
A supposed misrepresentation of Bomberg’s work and career in a catalogue text for a show of Holden, Richmond, Mead and Creffield in Sweden in 1952 led to a split in the relationship between the two artists. Despite this Holden remained one of the most vociferous supporters of Bomberg's work and teaching. In 1958 Holden gave a radio talk titled ‘An artist as a teacher’ for the BBC Third Program which was the first time Bomberg’s relevance as a teacher had afforded national attention. Holden is well represented in A David Bomberg Legacy – The Sarah Rose Collection at the London South Bank University. A 1947 figure painting by Holden is in the collection of the Tate Britain.