Meaning of "to get stuffed"

This quote is a pun, because "get stuffed" is being used in two ways here.

"To get stuffed" is a slightly antiquated piece of slang with the same meaning as "F off!" or "Screw you!" It's an implication that someone is worthless or meaningless. (That's the American phrase, which is used in this quote: "Get Stuffed" in England simply means "Go away" or "Get lost", just not as politely)

Edit: Huh, this is about London? Okay, I guess the "get lost" meaning is being used here. They have the same basic idea of implying that the target of the phrase is worthless or meaningless.

The quote also refers to taxidermy, that is, the practice (art?) of stuffing dead animals full of gunk so that they look pretty.

It refers to the practice of Taxidermy. Of course, the animals can't stuff themselves, so telling the animals to get stuffed is just a technique used to make the entire situation sound more ridiculous.

@Jeremy is right to say it's a pun on the two meanings of get stuffed, one being the reference to taxidermy. But as a slang idiom it doesn't really mean Go away! in normal usage.

It means I don't care about you. It's often used in a more immediate fashion with the specific meaning I don't agree with what you just said, but the former clearly fits better here.

My own gut feeling, backed up by this chart, is that the slang usage is not at all "antiquated".

I'm native to the UK and live in London. Get stuffed was in common usage here years ago, but rarely used now, and it does indeed have a sexual connotation, so saying 'get stuffed' to someone meant, literally, 'go fuck yourself', an expression which I believe is more common in America.