How do you call out a listener who thinks he's fooling you with a phony English accent? You take the approach an AM talk show host did here years ago. I remember this happening twice, when callers claimed to be from London. Both times, the host asked, "Say, I've forgotten. Who's the prime minister over there?"
Both callers, caught off guard, responded with some variation of, "Um...It used to be Margaret Thatcher." "Yes, it did," the host responded. "Who is it now?"
As I recall, both callers hung up quickly.