Algernon was born on 9 October 1925 in Stockholm, Sweden, the son of head of department Carl Algernon and his wife Dagmar. He became acting sub-lieutenant in 1947 and was promoted to sub-lieutenant in 1949. Algernon did flight interaction education from 1955 to 1956 and completed the staff course at the Royal Swedish Naval Staff College from 1956 to 1957. Algernon was promoted to lieutenant in 1959, was a member of the 1961 Defense Commission and was staff adjutant in the Coastal Fleet from 1962 to 1964 and was a lecturer at the Swedish National Defence College from 1964 to 1967. He became a member of the Royal Swedish Society of Naval Sciences in 1965. He was promoted to commander of the 2nd rank in 1965 and to commander of the 1st rank in 1966 and was a member of the Navy Officer Investigation from 1969 to 1971 when he was promoted to captain. Algernon was commanding officer of the 1st Destroyer Flotilla from 1971 to 1972 when he was promoted to captain of the 1st rank. He was vice chief at the staff of Eastern Military Area from 1972 to 1974 and chief of Section 2 in the Defence Staff from 1974 to 1978 when he was promoted to rear admiral. Algernon served afloat on various types of ships in the Swedish Navy during 1947-55, 1958-64, 1968-69 and 1971-72. He was head of the Military Office of the Minister of Defence from 1978 to 1979 and its subsequent agency, the Ministry of Defence's International Unit from 1979 to 1981 when he was appointed head of the National Swedish War Materials Inspectorate, a governmental agency tasked with supervising and revise exports of war materiel to foreign countries.
At the outbreak of the Bofors scandal in the late 1980s he became one of the leading investigators into the scandal despite the fact that he was a personal friend of the CEO of Bofors, Martin Ardbo, for many years. Algernon died when he was hit by a train at the Stockholm metro station T-Centralen on 15 January 1987. Earlier on the day he had a meeting with the CEO of Nobel Industrier, Anders Carlberg, about the allegations of smuggling against the company. During the conversation, Carlberg had told Algernon about an internal investigation which had confirmed that smuggling had existed. Due to Algernon's position as a leading investigator of the Bofors scandal, it was speculated that he might have been assassinated. The subsequent investigation into his death, which ended on 11 March 1987, concluded that he had committed suicide.