There has been much discussion over the origin of the term, "Pom" or "Pommie". One theory is that it derives from "Pomegranate", because newly arrived English people were often burned red by the hot Aussie sun, leading to claims that their faces resembled pomegranates. Another theory is as Nordsee suggests, an acronym from Prisoners of His Majesty". I don't think anyone really knows.
Whatever the origin, it is certainly no more derogatory than referring to New Zealanders as Kiwis, Americans as Yanks, or even Australians as Aussies.
Many English still think of Aussies as being descendants of convicts, and a small number of the population can claim that "distinction", but the vast majority, myself included, are descended from free settlers. What also needs to be remembered is many of the convicts were deported, by an extremely harsh penal system, for very minor crimes, including stealing bread to feed their starving families.
Peter.