| Dr Cecil Fifoot FBA | Year of birth 1899 | Year of death 1975 | Year elected 1954 | Fellowship category UK |
| Professor Jan Filip FBA | Year of birth 1900 | Year of death 1981 | Year elected 1976 | Fellowship category Corresponding |
| Professor Jean Lucien Antoine Filliozat FBA | Year of birth 1906 | Year of death 1982 | Year elected 1972 | Fellowship category Corresponding |
| Professor John Findlay FBA | Year of birth 1903 | Year of death 1987 | Year elected 1956 | Fellowship category UK |
| Professor Samuel Finer FBA | Year of birth 1915 | Year of death 1993 | Year elected 1982 | Fellowship category UK |
| Sir Moses Finley FBA | Year of birth 1912 | Year of death 1986 | Year elected 1971 | Fellowship category UK |
| Sir Charles Firth FBA | Year of birth 1857 | Year of death 1936 | Year elected 1903 | Fellowship category UK |
| Professor Sir Raymond Firth FBA | Year of birth 1901 | Year of death 2002 | Year elected 1949 | Fellowship category UK |
| Professor Fritz Fischer FBA | Year of birth 1900 | Year of death 2000 | Year elected 1971 | Fellowship category Corresponding |
| Dr Henry Fischer FBA | Year of birth 1923 | Year of death 2006 | Year elected 1996 | Fellowship category Corresponding |
| Professor Eli Fischer-Jørgensen FBA | Year of birth 1911 | Year of death 2010 | Year elected 1995 | Fellowship category Corresponding |
| Right Hon Herbert Albert Laurens Fisher OM, FBA, FRS | Year of birth 1865 | Year of death 1940 | Year elected 1907 | Fellowship category UK |
| Dr Marc Fitch CBE, Hon FBA | Year of birth 1908 | Year of death 1994 | Year elected 1978 | Fellowship category Honorary |
| Rt Hon Lord Edmond Fitzmaurice PC, FBA | Year of birth 1846 | Year of death 1935 | Year elected 1914 | Fellowship category UK |
| Professor James Fitzmaurice-Kelly FBA | Year of birth 1857 | Year of death 1923 | Year elected 1906 | Fellowship category UK |
| Dr Josef Fleckenstein FBA | Year of birth 1919 | Year of death 2004 | Year elected 1991 | Fellowship category Corresponding |