I am honestly trying to figure out what you are arguing here. GGP didn't say something like "This is what everyone in England sounds like: ..."

Isn't that what a caricature is supposed to do?

Here we have a caricature which is irritating because it's off the mark. I demand better mockery.

Is Birmingham accent bad mockery?

It's oddly specific mockery, like Ozzy is England's international representative. I don't know, maybe he is. But I doubt Birmingham even inspired the meme, this is probably a caricature of Dick Van Dyke more than anyone.

To be fair, Brits seem to think New Yorkers go "oi" and they don't really either.