I think the standard for bad accents is Kevin Costner in Robin Hood. Hell, I think halfway through the movie, he just gave up on it all together.
I read somewhere that the plan at one point was to not worry about the accent while shooting and they would just have Costner redub all of his lines with a British accent in post. But then they ran out of time, so they weren't able to dub any of it.
Russell Crowe in Robin Hood (2010) - Scottish, Irish, anyone's guess - something about the subject matter invites bad accents for some reason.
It's really weird how hardly any of the actors in that movie are actually English, despite the fact that, IIRC, it was shot in England. Crowe & Blanchett are both Australian. Max Von Sydow is Swedish. Oscar Isaac was born in Guatemala to a Cuban father and was raised in Florida. Most of the Merry Men are American or Canadian (except for true Brit Mark Addy as Friar Tuck). The few genuinely British actors in the film--Mark Strong, Eileen Atkins, Matthew MacFadyen--are all playing characters with some element of French ancestry.
I'm not sure I can speak to the veracy of the accent, but it's kinda disturbing seeing Michael Caine do a New England accent in
The Cider House Rules.
Nicola Bryant was inconsistent when she played American companion Peri on
Doctor Who in the 1980s. Mostly, her accent was passable, although they often failed to capture an accurate American vocabulary. (No one from the U.S. calls it "The States.")
Worse were the actors that played Peri's family when we first met her in "Planet of Fire." I think they were going for a general western-American accent. (They were supposed to be from New Mexico, IIRC.) Instead, at best, they might have been able to pass as some incredibly aristocratic family from Boston.
The 1950s
Sherlock Holmes TV show with Ronald Howard & H. Marion Crawford is a very rich source for bad accents. For some reason, it was shot in Paris. So other than Holmes, Watson, & Inspector Lestrade, all of the guest actors are French, many of whom struggle quite a bit speaking English at all, to say nothing of pulling off an English accent. There's one episode in particular, "The Case of Harry Crocker," where you've got the truly bizarre sound of an actor with a strong French accent trying to fake an extremely corny Cockney accent. (They also can't seem to agree on whether his last name is "Crocker" or "Croker.")