| Mr Hugh Honour FBA | Year of birth 1927 | Year of death 2016 | Year elected 1986 | Fellowship category Corresponding |
| Professor Roger Hood FBA | Year of birth 1936 | Year of death 2020 | Year elected 1992 | Fellowship category UK Emeritus |
| Mr Sinclair Hood FBA | Year of birth 1917 | Year of death 2021 | Year elected 1983 | Fellowship category UK |
| Professor Keith Hopkins FBA | Year of birth 1934 | Year of death 2004 | Year elected 1984 | Fellowship category UK |
| Professor Dr Erik Hornung FBA | Year of birth 1933 | Year of death 2022 | Year elected 2000 | Fellowship category Corresponding |
| Professor Robin Horton FBA | Year of birth 1932 | Year of death 2019 | Year elected 1996 | Fellowship category Corresponding |
| Professor William Hoskins CBE, FBA | Year of birth 1908 | Year of death 1992 | Year elected 1969 | Fellowship category UK |
| Professor Chihiro Hosoya FBA | Year of birth 1920 | Year of death 2011 | Year elected 1995 | Fellowship category Corresponding |
| Professor Sir Michael Howard OM, CH, CBE, FBA | Year of birth 1922 | Year of death 2019 | Year elected 1970 | Fellowship category UK Emeritus |
| Revd Dr Wilbert Francis Howard FBA | Year of birth 1880 | Year of death 1952 | Year elected 1949 | Fellowship category UK |
| Professor Anne Hudson FBA | Year of birth 1938 | Year of death 2021 | Year elected 1988 | Fellowship category UK |
| Professor Glyn Humphreys FBA | Year of birth 1954 | Year of death 2016 | Year elected 2009 | Fellowship category UK |
| Professor Dr Herbert Hunger FBA | Year of birth 1914 | Year of death 2000 | Year elected 1987 | Fellowship category Corresponding |
| Professor Arthur Surridge Hunt FBA | Year of birth 1871 | Year of death 1934 | Year elected 1913 | Fellowship category UK |
| Dr Richard Hunt FBA | Year of birth 1908 | Year of death 1979 | Year elected 1961 | Fellowship category UK |
| Professor George Hunter FBA | Year of birth 1920 | Year of death 2008 | Year elected 1988 | Fellowship category Corresponding |