| Professor Rodney Hilton FBA | Year of birth 1916 | Year of death 2002 | Year elected 1977 | Fellowship category UK |
| Professor Gertrude Himmelfarb FBA | Year of birth 1922 | Year of death 2019 | Year elected 1987 | Fellowship category Corresponding |
| Professor Nikolaus Himmelmann FBA | Year of birth 1929 | Year of death 2013 | Year elected 1986 | Fellowship category Corresponding |
| Professor Robert Hinde CBE, FRS, Hon FBA | Year of birth 1923 | Year of death 2016 | Year elected 2002 | Fellowship category Honorary |
| Professor Sir Harry Hinsley OBE, FBA | Year of birth 1918 | Year of death 1998 | Year elected 1981 | Fellowship category UK |
| Professor Albert Hirschman FBA | Year of birth 1914 | Year of death 2012 | Year elected 1984 | Fellowship category Corresponding |
| Professor Michael Hirst FBA | Year of birth 1933 | Year of death 2017 | Year elected 1983 | Fellowship category UK Emeritus |
| Professor Leonard Trelawny Hobhouse FBA | Year of birth 1864 | Year of death 1929 | Year elected 1925 | Fellowship category UK |
| Professor Eric Hobsbawm CH, FBA | Year of birth 1917 | Year of death 2012 | Year elected 1976 | Fellowship category UK Emeritus |
| Dr Anthony Hobson FBA | Year of birth 1921 | Year of death 2014 | Year elected 1992 | Fellowship category UK Emeritus |
| Dr Thomas Hodgkin FBA | Year of birth 1831 | Year of death 1913 | Year elected 1902 | Fellowship category UK |
| Dr Shadworth Hollway Hodgson FBA | Year of birth 1832 | Year of death 1912 | Year elected 1902 | Fellowship category UK |
| Professor Carsten Høeg FBA | Year of birth 1896 | Year of death 1961 | Year elected 1953 | Fellowship category Corresponding |
| Professor Henry Hoenigswald FBA | Year of birth 1915 | Year of death 2003 | Year elected 1986 | Fellowship category Corresponding |
| Professor Harald Hoffding FBA | Year of birth 1843 | Year of death 1931 | Year elected 1907 | Fellowship category Corresponding |
| Professor Stanley Hoffmann FBA | Year of birth 1928 | Year of death 2015 | Year elected 1996 | Fellowship category Corresponding |