Campbell was born in Southsea, Hampshire on 15 June 1912.

As a young boy, he was influenced by his father, an army officer, birds-nester and egg-collector, who later became the British Army's Inspector of Physical Training. After education at Winchester College, he studied at the University of Edinburgh, obtaining a BSc in forestry. He later gained a doctorate in comparative bird studies, so becoming one of the first field naturalists to also be a trained scientist. In 1938, he married Margaret Gibson-Hill, herself a writer, with whom he had two sons and one daughter.

From 1936 to 1948, he was a teacher and university lecturer. After World War II, he brought the work of sound recordist Ludwig Koch to the attention of the BTO. In 1948, Campbell was appointed the first full-time secretary of the BTO, a post he held until 1959.

He served on the panel of the Wildlife Collection with Julian Huxley, and was active in the British Ornithologists' Union, the British Ecological Society, and conservation bodies. He conducted a pioneering study of the pied flycatcher at the Nagshead woodland reserve, Gloucestershire. He made radio and television broadcasts relating to natural history for the BBC during the 1950s.

In April 1959, despite his having had no previous experience as a producer, he was appointed senior producer at the BBC Natural History Unit in Bristol, a position he held until 1962. He died on 9 January 1993 in Witney, Oxfordshire.