Randal Mathews Burdon was born at North Ambersham, near Haslemere, Sussex, England, on 4 August 1896, the son of Mildred Yatman and her husband, Cotsford Mathews Burdon, described as being of independent means. In 1902 the Burdons emigrated to New Zealand, establishing a sheep farm at Woodbury, Geraldine. Randal attended Waihī School in Winchester and Christ's College, Christchurch. He left for England in 1914 hoping to study law, but his plans were interrupted by the outbreak of war. He was commissioned in England as second lieutenant in the Queen's Royal West Surrey Regiment and served in France and Italy. Twice grievously wounded, he was decorated with the Military Cross. In 1918 he abandoned plans to study law at the University of Cambridge and became a captain in the 13th Duke of Connaught's Bengal Lancers on India's north-west frontier.
Burdon left the army in 1922 and returned to New Zealand. He established a farm at Woodbury, and a high-country sheep run. While on leave at Woodbury two years previously he had married Jean Stewart Bowden, on 8 April 1920. They had a son and a daughter, but were divorced in 1932.
During his schooldays Burdon had excelled at team sports. At Woodbury he played polo and joined the South Canterbury Hunt. Large, powerfully built and with small, shrewd, twinkling eyes, he was considered 'sophisticated, interesting' and with a 'racy sense of humour'. His peers noted the tough craggy look, strong presence and resonant voice. Of theatrical bent, he lined his hallway with cavalry lances – mementoes of his India days – and sometimes displayed a slashed and bloody First World War tunic. He gardened well, collected rare editions and read widely.
In the 1930s Burdon turned to writing. History was his forte, the Hocken Library his favourite research institution. High country, published in 1938, examined the triumph of pastoralism in colonial Canterbury. New Zealand, Ngaio Marsh's 1942 contribution to the patriotic 'Britain in pictures' series, contained Burdon's summary of the nation's history. The last volume conceived at Woodbury, The life and times of Sir Julius Vogel, was overshadowed by three slim volumes of biographical essays, New Zealand notables. The selection of subjects was extremely varied, ranging from the missionary Thomas Kendall to the Dunedin eccentric J. G. S. Grant. The extent of his research, his shrewd perception of character and his unobtrusive irony make the books a notable contribution to New Zealand biographical writing.
Burdon's one novel, Outlaw's progress (1943), examined the grim economic realities that drove Owen Marley, a Man Alone figure, to violence. The depiction of a starve-acre soldier settlement was well realised; dialogue and characterisation were not, and the author would exclude this 'damn bad novel' from the canon of his works.
By 1948 illness had left Burdon lame and reliant on a walking stick. He moved to Karori, Wellington, and was contracted by the War History Branch of the Department of Internal Affairs to write a Second World War unit history. He was a frequent researcher at branch headquarters, where his military background endeared him to staff members who were war veterans. Editors appreciated his reliability. The very readable 24 Battalion was published in 1953.
King Dick (1955), Burdon's biography of Richard John Seddon, was well received, and was followed a year later by Scholar errant, which traced the multi-faceted career of the eccentric Christchurch professor Alexander Bickerton. The new dominion, a study of life between the wars, was published in 1965. Although a valuable and perceptive study, it was criticised for its neglect of archives and dependence on newspapers and secondary sources. However, Burdon was now very conscious of his physical incapacity and fearful of mental deterioration. The most that he could manage was to drive to the parliamentary library, settle in the reading room, take a small notebook from his deep coat pocket and, in almost crabbed handwriting, transcribe newspaper material.
Burdon was a methodical, persistent researcher whose dry prose style concealed his colourful personality. As biographer he emphasised the relationship of the individual to the era. He wrote for periodicals such as Kōrero and Landfall, was a New Zealand Listener book reviewer and contributed to A. H. McLintock's An encyclopaedia of New Zealand (1966).
Usually an excellent companion, he was also fearlessly independent and sometimes abrupt in manner. He held annual salon parties for military friends and Wellington intellectuals. At small dinner parties with friends from academia, Burdon listened carefully and enjoyed debate. However, the high point of such gatherings was the host's conversation, 'anecdotal, full of strange characters and adventures, and filled out with parable and homely aphorism'.
After a period of intermittent illness, Randal Burdon died of coal gas poisoning at his home in Wellington on 28 or 29 November 1965. It was unclear whether death was the result of accident or suicide. He was survived by his son and daughter.