It is now pretty well accepted that the pomegranate theory is close to the truth,though there’s a slight twist to take note of. H J Rumsey wrote about it in 1920 in the introduction to his book The Pommies, or New Chums in Australia. He suggested that the word began life on the wharves in Melbourne as a form of rhyming slang. An immigrant was at first called a Jimmy Grant (was there perhaps a famous real person by that name around at the time?), but over time this shifted to Pommy Grant, perhaps as a reference to pomegranate, because the new chums did burn in the sun. Later pommy became a word on its own and was frequently abbreviated still further. The pomegranate theory was also given some years earlier in The Anzac Book of 1916.
Whatever your beliefs about this one, what seems to be true is that the term is not especially old, dating from the end of the nineteenth century at the earliest, certainly not so far back as convict ship days
