I believe there is generally a more negative connotation associated with putting on an Asian accent. Typically, immigrant, Asian minorities have an issue with speaking English correctly. It isn't that they don't understand the language, but rather certain sounds get mixed up. Intolerant types tend to belittle the intelligence of these people, because of this. This is rather common place, and isn't something that is exclusive to Asians. Anyone with a thick accent that has trouble with pronouncing English words is typically met with prejudice, impatience, and intolerance on a weekly, if not daily, basis. So, when one decides to mimic an Asian accent, it is often seen in a poor light, because an Asian person is often mocked in the very same way. A person will put on an exaggerated Asian accent, and mock the poor fellow (often behind their backs).
Now, a British or Australian accent is normally spoken in English. There's no feelings of sympathy. It simply isn't thought of, because both the British and Australians speak English naturally-- they're apart of the club. They know English, so there aren't any frustrations over a language barrier.
However, this is not to make light of the issue at all. People will make fun of any accent for any given reason. Sometimes it's light-hearted, and other times it isn't. We just have a tendency, as a whole, to mock or ridicule the things that aren't normal relative to our own culture.
What Beguile's Mistress as written above also factors heavily into this as well, I believe.