As an American, I find it most noticeable/funny in Helen Mirren's Fast & Furious franchise role. You can tell she's having a blast putting on the intentionally worst working class accent she can (in a way that it sometimes seems like she assumes Americans aren't in on the joke and it is mostly just for herself) to fit her role as Jason Statham's "mum", and there are definite fun moments of "Is she intentionally parodying Michael Caine here?" that do give me (as an American) silly, brief moments of "Americans still think that sounds posh", plus it does serve to more directly connect Statham's accent to Caine's. I don't think a lot of Americans notice how close they are and yet do notice that Statham and Caine have very different stereotypes in American cinema.