POME stands for "Prisoner Of Mother England". I believe originally it was meant to describe the British prisoners that were sent to Australia, but now the Australians have turned it around to designate anyone from England. I think a variation of it was POHM - "Prisoner Of His Majesty".
The term POM or pommy is thought by some Brits living in Australia to be offensive or demeaning, whereas other Brits find it harmless and amusing. It all depends on context...for instance, if Julia had someone say to her "You bloody damn pome!", she could respond with "May all your chooks turn into emus and kick your dunny down!"
