| Professor Walter Henning FBA | Year of birth 1908 | Year of death 1967 | Year elected 1954 | Fellowship category UK |
| Professor Louis Henry FBA | Year of birth 1900 | Year of death 1991 | Year elected 1972 | Fellowship category Corresponding |
| Professor Sir Bob Hepple QC, FBA | Year of birth 1934 | Year of death 2015 | Year elected 2003 | Fellowship category UK Emeritus |
| Professor Charles Harold Herford FBA | Year of birth 1853 | Year of death 1931 | Year elected 1926 | Fellowship category UK |
| Professor Nils Herlitz FBA | Year of birth 1888 | Year of death 1978 | Year elected 1971 | Fellowship category Corresponding |
| Professor Ernst E Herzfeld FBA | Year of birth 1879 | Year of death 1948 | Year elected 1947 | Fellowship category Corresponding |
| Professor Mary Hesse FBA | Year of birth 1924 | Year of death 2016 | Year elected 1971 | Fellowship category UK Emeritus |
| Professor Jacques Heurgon FBA | Year of birth 1903 | Year of death 1995 | Year elected 1972 | Fellowship category Corresponding |
| Professor Robert Heuston FBA | Year of birth 1923 | Year of death 1995 | Year elected 1988 | Fellowship category Corresponding |
| Professor George Dawes Hicks FBA | Year of birth 1862 | Year of death 1941 | Year elected 1927 | Fellowship category UK |
| Sir John Hicks FBA | Year of birth 1904 | Year of death 1989 | Year elected 1942 | Fellowship category UK |
| Professor James Higginbotham FBA | Year of birth 1941 | Year of death 2014 | Year elected 1995 | Fellowship category UK |
| Professor Alexander Pearce Higgins CBE, KC, FBA | Year of birth 1865 | Year of death 1935 | Year elected 1928 | Fellowship category UK |
| Professor James Higgins FBA | Year of birth 1939 | Year of death 2021 | Year elected 1998 | Fellowship category UK Emeritus |
| Dr Reynold Higgins FBA | Year of birth 1916 | Year of death 1993 | Year elected 1972 | Fellowship category UK |
| Professor Alan Hill FBA | Year of birth 1931 | Year of death 2015 | Year elected 1994 | Fellowship category UK Emeritus |