| Professor Ernst Badian FBA | Year of birth 1925 | Year of death 2011 | Year elected 1965 | Fellowship category UK Emeritus |
| Dr Cyril Bailey CBE, FBA | Year of birth 1871 | Year of death 1957 | Year elected 1933 | Fellowship category UK |
| Professor David Bailey FBA | Year of birth 1917 | Year of death 2005 | Year elected 1958 | Fellowship category UK |
| Sir Harold Bailey FBA | Year of birth 1899 | Year of death 1996 | Year elected 1944 | Fellowship category UK |
| Dr Anthony Baines FBA | Year of birth 1912 | Year of death 1997 | Year elected 1980 | Fellowship category UK |
| Professor Roland H Bainton FBA | Year of birth 1894 | Year of death 1984 | Year elected 1973 | Fellowship category Corresponding |
| Professor Dr Kurt Baldinger FBA | Year of birth 1900 | Year of death 2007 | Year elected 1988 | Fellowship category Corresponding |
| Professor John Baldwin FBA | Year of birth 1929 | Year of death 2015 | Year elected 1992 | Fellowship category Corresponding |
| Right Hon the Earl Arthur Balfour KG, PC, FRS, OM, FBA | Year of birth 1848 | Year of death 1930 | Year elected 1902 | Fellowship category UK |
| Professor Luigi Balsamo FBA | Year of birth 1926 | Year of death 2012 | Year elected 2000 | Fellowship category Corresponding |
| Dr John Balsdon FBA | Year of birth 1901 | Year of death 1977 | Year elected 1967 | Fellowship category UK |
| Count Ugo Balzani FBA | Year of birth 1847 | Year of death 1916 | Year elected 1904 | Fellowship category Corresponding |
| Dr Caroline Hammond Bammel Bammel FBA | Year of birth 1940 | Year of death 1995 | Year elected 1994 | Fellowship category UK |
| Professor Ofer Bar-Yosef FBA | Year of birth 1937 | Year of death 2020 | Year elected 2005 | Fellowship category Corresponding |
| Mr Eric Arthur Barber FBA | Year of birth 1888 | Year of death 1965 | Year elected 1936 | Fellowship category UK |
| Professor Andrew Barker | Year of birth 1943 | Year of death 2021 | Year elected 2005 | Fellowship category UK Emeritus |