| Sir Karl Popper CH, FRS, FBA | Year of birth 1902 | Year of death 1994 | Year elected 1958 | Fellowship category UK |
| Professor Edith Porada FBA | Year of birth 1900 | Year of death 1994 | Year elected 1977 | Fellowship category Corresponding |
| Professor Roy Porter FBA | Year of birth 1946 | Year of death 2002 | Year elected 1994 | Fellowship category UK |
| M Georges Posener FBA | Year of birth 1906 | Year of death 1988 | Year elected 1986 | Fellowship category Corresponding |
| Sir Michael Postan FBA | Year of birth 1899 | Year of death 1981 | Year elected 1959 | Fellowship category UK |
| Professor John Percival Postgate FBA | Year of birth 1853 | Year of death 1926 | Year elected 1907 | Fellowship category UK |
| Mr Philip Pouncey CBE, FBA | Year of birth 1910 | Year of death 1990 | Year elected 1975 | Fellowship category UK |
| Professor Roscoe Pound FBA | Year of birth 1870 | Year of death 1964 | Year elected 1940 | Fellowship category Corresponding |
| Professor Joseph Powell FBA | Year of birth None | Year of death 2022 | Year elected 2001 | Fellowship category Corresponding |
| Professor Harold Powers FBA | Year of birth 1928 | Year of death 2007 | Year elected 1999 | Fellowship category Corresponding |
| Sir Maurice Powicke FBA | Year of birth 1879 | Year of death 1963 | Year elected 1927 | Fellowship category UK |
| Professor Sigbert Prais FBA | Year of birth 1928 | Year of death 2014 | Year elected 1985 | Fellowship category UK |
| Professor Siegbert Prawer FBA | Year of birth 1925 | Year of death 2012 | Year elected 1981 | Fellowship category UK Emeritus |
| Mlle Claire Préaux FBA | Year of birth 1904 | Year of death 1979 | Year elected 1956 | Fellowship category Corresponding |
| Professor Allan Pred FBA | Year of birth 1936 | Year of death 2007 | Year elected 2005 | Fellowship category Corresponding |
| Professor Edgar Prestage FBA | Year of birth 1869 | Year of death 1951 | Year elected 1940 | Fellowship category UK |