| Professor Geoffrey Hartman FBA | Year of birth 1929 | Year of death 2016 | Year elected 2000 | Fellowship category Corresponding |
| Professor Francis Haskell FBA | Year of birth 1928 | Year of death 2000 | Year elected 1971 | Fellowship category UK |
| Professor Charles Homer Haskins FBA | Year of birth 1870 | Year of death 1937 | Year elected 1926 | Fellowship category Corresponding |
| Professor Arthur Hatto FBA | Year of birth 1910 | Year of death 2010 | Year elected 1991 | Fellowship category UK |
| Professor Ragnhild Hatton FBA | Year of birth 1913 | Year of death 1995 | Year elected 1993 | Fellowship category UK |
| Professor Shiro Hattori FBA | Year of birth 1908 | Year of death 1995 | Year elected 1976 | Fellowship category Corresponding |
| Professor Francis John Haverfield FBA | Year of birth 1860 | Year of death 1919 | Year elected 1904 | Fellowship category UK |
| Professor Louis Havet FBA | Year of birth 1849 | Year of death 1925 | Year elected 1917 | Fellowship category Corresponding |
| Professor Bohuslav Havranek FBA | Year of birth 1893 | Year of death 1978 | Year elected 1977 | Fellowship category Corresponding |
| Professor Charles Hawkes FBA | Year of birth 1905 | Year of death 1992 | Year elected 1948 | Fellowship category UK |
| Professor David Hawkins FBA | Year of birth None | Year of death 2024 | Year elected 1993 | Fellowship category UK |
| Professor Katherine Hawley FBA | Year of birth 1971 | Year of death 2021 | Year elected 2020 | Fellowship category UK |
| Sir Ralph Hawtrey CB, FBA | Year of birth 1879 | Year of death 1975 | Year elected 1935 | Fellowship category UK |
| Professor Denys Hay FBA | Year of birth 1915 | Year of death 1994 | Year elected 1970 | Fellowship category UK |
| Professor Friedrich Hayek CH, FBA | Year of birth 1899 | Year of death 1992 | Year elected 1944 | Fellowship category UK |
| Professor Jack Hayward FBA | Year of birth 1931 | Year of death 2017 | Year elected 1990 | Fellowship category UK Emeritus |