Sir Francis Brian Anthony Rundall GCMG OBE (11 September 1908 – 7 July 1987) was a British diplomat. He served as British Ambassador to Israel from 1957 to 1959 and British Ambassador to Japan from 1963 to 1967.

Rundall was born in Kent, England^[1] on 11 September 1908. He was educated at Marlborough College, followed by the University of Cambridge^[2] and the University of Berlin.^[1]

Rundall entered the Diplomatic Service in 1930^[2] as a consular officer.^[1] He subsequently served as Head of the North American Department of the Foreign Office from 1947 to 1948, Head of the United Nations (Economic and Social) Department and Refugee Department of the Foreign Office from 1948 to 1949, an inspector from 1949 to 1953, New York Consul-General from 1953 to 1957, Ambassador to Israel from 1957 to 1959, Deputy Under-Secretary for Foreign Affairs and Chief Clerk from 1959 to 1963 and Ambassador to Japan from 1963 to 1967.^[3]

He was appointed a GCMG on 1 January 1968.^[4]

Rundall married Mary Syrett on 26 January 1935.^[5] His hobby was trout fishing. By 1956 he lived at 1 Beekman Place in New York and had two children being schooled in England.^[1] He died on 7 July 1987.^[2]