Well, it varies. The best are the ones where you don't realise they're not British, like Alexis Denisof or Kyle Soller off of Poldark. I'm sure there are equivalents in the US, but you don't notice because you don't clock they're not American.

Denisof (like Gillian Anderson, who was raised there) had the advantage of having lived there for years. Stuff made when he was still a UK resident but supposed to be an American character is hilarious because, at the time, his US accent was as god-awful as, say, Kenneth Branagh's. Which is pretty bad.

I watched a cute-if-predictable rom-com a few months back called "Man Up" and thought Lake Bell (who's from NYC) had a pretty decent British accent to my admittedly untrained ears. You can hear her from the trailer: [link]

(If you're interested in the watching the film, the trailer pretty much gives away the entire plot. But hey, it's a rom-com so you know it's gonna end a certain way.)

There was a movie in the 90's called Judas Kiss that had Alan Rickman and Emma Thompson trying to do New Orleans accents without any success. It was really awful. I see now that Simon Baker was in, too, but I Have no recollection of his attempt.

Speaking of Baker, I never guessed that Owain Yeoman was British until he turned up one time on Midsomer Murders using his (presumably) real accent. Same thing for Damien Lewis. I never picked up his real accent at all in either Band of Brothers or Life.

New Orleans accents are always terrible.

Simon Baker is pretty good, but there's some particular vowel-consonant combination that gives him away. I forget what, but it's something to do with an American rrrrrrr.

Agreed on Owain Yeoman and Damian Lewis. (Damian Lewis. Yum.)

Edit: Oh, and Rose McIvwer on iZombie is flawless. I had no clue, and I can usually pick up on it.

I watched a cute-if-predictable rom-com a few months back called "Man Up" and thought Lake Bell (who's from NYC) had a pretty decent British accent to my admittedly untrained ears.

Well she did direct In a World... so I figure she has access to good vocal coaches. I highly recommend both that one and Man Up, which is very cute. I particularly liked the dynamics of the older couples in the latter.

Agreed on Owain Yeoman and Damian Lewis.

My theory is all (or at least most) of the British actors who cannot manage a good American accent stay in Britain and do tv and theater there. It's a relative few who can make the leap to the US.

Considering how good the British accent tends to sound to American ears, why not just change the character to a Brit if one of those actors gets cast?

Has Tony Head ever done an American accent?

Yes, on the TV show Dominion, a couple years ago.

Not good.

The guy who plays Rick Grimes. I don't watch the show but my husband does and I had to ask what was up with that accent.