| Professor John Burrow FBA | Year of birth 1932 | Year of death 2017 | Year elected 1986 | Fellowship category UK Emeritus |
| Professor Thomas Burrow FBA | Year of birth 1909 | Year of death 1986 | Year elected 1970 | Fellowship category UK |
| Sir Cyril Burt FBA | Year of birth 1883 | Year of death 1971 | Year elected 1950 | Fellowship category UK |
| Professor John Bagnell Bury FBA | Year of birth 1861 | Year of death 1927 | Year elected 1902 | Fellowship category UK |
| Professor John Nash Douglas Bush FBA | Year of birth 1896 | Year of death 1983 | Year elected 1960 | Fellowship category Corresponding |
| Dr Geoffrey Bushnell FBA | Year of birth 1903 | Year of death 1978 | Year elected 1970 | Fellowship category UK |
| Mr Samuel Henry Butcher FBA | Year of birth 1850 | Year of death 1910 | Year elected 1902 | Fellowship category UK |
| Sir David Butler FBA CBE | Year of birth None | Year of death 2022 | Year elected 1994 | Fellowship category UK |
| Professor Marilyn Butler FBA | Year of birth 1937 | Year of death 2014 | Year elected 2002 | Fellowship category UK Emeritus |
| Professor Noel George Butlin FBA | Year of birth 1921 | Year of death 1991 | Year elected 1976 | Fellowship category Corresponding |
| Professor John Butt FBA | Year of birth 1906 | Year of death 1965 | Year elected 1961 | Fellowship category UK |
| Sir Herbert Butterfield FBA | Year of birth 1900 | Year of death 1979 | Year elected 1965 | Fellowship category UK |
| Mr Ingram Bywater FBA | Year of birth 1840 | Year of death 1914 | Year elected 1902 | Fellowship category UK |