| 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 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 |
| Professor John N Hazard FBA | Year of birth 1900 | Year of death 1995 | Year elected 1973 | Fellowship category Corresponding |
| Professor Harold Dexter Hazeltine FBA | Year of birth 1871 | Year of death 1960 | Year elected 1924 | Fellowship category UK |
| Professor Seamus Heaney FBA | Year of birth 1939 | Year of death 2013 | Year elected 1999 | Fellowship category Corresponding |
| Sir Thomas Heath KCB, KCVO, FBA | Year of birth 1861 | Year of death 1940 | Year elected 1932 | Fellowship category UK |