Maybe I just don't get around enough, but I have never heard any English accent that Australian or New Zealander accents sound like. Mind you, they do sound like English accents. Just not like any actual extant one.
As to Canadian accents, given the regional variances in American English, even many Americans (particularly from the Southeast) can't distinguish it from a general Northern-Midwest (like what you'd get in Minnesoooota). In my experience though, its definitely there. Michael Hogan (of BSG fame) probably has one of the strongest Canadian accents you'll ever hear. If you use his speech patterns as a base and extrapolate, then even people like Pamela Anderson will suddenly sound unmistakeably Canadian. There are, of course, regional distinctions even there and I find the Newfoundland accent particularly perplexing (I'm guessing it's more of a dialect than accent).
Listen to any interviews with the cast and crew behind the LOTR movies and the whole range of English accents from across the planet are pretty much all there, except maybe South African and the non-British dialectal ones (West Indian, South Asian, etc.). It makes a good basis for comparison. You've got several different English accents, some Scottish ones, a couple of American ones, Welsh, Canadian, Australian and Kiwi. I'm sure that there's at least one Irish in there somewhere. It's like an English accent pu pu platter.