Rudolph Albert Peters was born in Kensington in 1889, the son of Dr. A.E. Peters. He was educated at Warden House preparatory school, Wellington College, and Gonville and Caius College, Cambridge, and became a research Fellow of Caius in 1911.

In 1913 he went to St. Bartholomew's Hospital to complete his medical training, and after graduating in 1915 he joined the Royal Army Medical Corps. His service in the field gained him the Military Cross and bar. In 1917 Peters married Frances Williamina. Earlier in the same year he was recalled to start work on chemical defence under J. (later Sir Joseph) Barcroft at Porton Down. He remained there for the rest of the war. He gained his MD in 1919.

After the First World War, Peters returned to Cambridge where he was elected to a Fellowship at his old college and joined the Department of Biochemistry as Senior Demonstrator.

In 1923 he was appointed to the recently founded Whitley Chair of Biochemistry at Oxford University, a position he held until 1954. At that time the Biochemistry Department was accommodated in 3 rooms in the Department of Physiology, but Peters was asked to submit estimates for a new building with extended staff and facilities. This was duly completed in 1927 with the aid of a generous grant from the Rockefeller Foundation.

Much of his early work in the department was concerned with large-scale attempts to prepare vitamin B (thiamine) from yeast, and with studies of its nature and mode of action. This led him to the demonstration of a 'biochemical lesion' in the pyruvate oxidase system of pigeons suffering from vitamin B1 deficiency.

With the outbreak of the Second World War, Peters was invited by the Ministry of Supply to engage in research on the medical aspects of defence against chemical weapons. He therefore organised a small group of workers whose investigations led to considerable information about the action of mustard gas and to the discovery of British Anti-Lewisite (BAL). The initial members of this team were H.M. Sinclair and R.H.S. Thompson (working on arsenicals) and E. Holiday, A.G. Ogston, J.St.L. Philpot, L.A. Stocken and R.W. Wakelin (on mustard gas). In the later years of the war, work was also done on burns.

The work on F-compounds (in particular the biochemical mechanism involved in fluoroacetate poisoning) began after the Second World War as an extension of Peters's continued interest in toxicological problems.

After his retirement from Oxford in 1954, Peters moved to the Agricultural Research Council Animal Physiology Unit at Babraham, where he remained for five years. He then join the Cambridge University Biochemistry Department as Senior Visiting Fellow in 1959. Here he continued his research on F-compounds and other related problems, including a collaboration with J.M. Walshe in a study of the mechanisms of copper toxicity for brain enzymes. He remained at Cambridge until his final retirement in July 1980.

Peters was elected a fellow of the Royal Society in 1935, received its royal medal in 1949, and delivered its Croonian lecture in 1952. In that year he was knighted and became FRCP. He was elected honorary fellow of Gonville and Caius College, and of Trinity College, Oxford. As well as his university duties in research, teaching, and administration, he was adviser to the Medical Research Council, the Ministry of Supply, and St. Bartholomew's Hospital. From 1958 to 1961 he served as President of the International Council of Scientific Unions. He died in Cambridge on 29 January 1982.