Hugh Laurie was the big shocker for me, but not because I saw him in House and thought he was American. I've been a huge fan of his for decades (Blackadder, Jeeves & Wooster, A bit of Fry & Laurie) and when I saw him it was like watching a cat bark. Not only that, but COMPLETELY convincing that it was perfectly normal for this cat to bark. Lol
On the flip side I was in London about 8 years ago and watched some made for TV movie that had an American character in it. The accent was laughable and he kept calling people "dog" 'cause that's clearly what all Americans call eachother.
So it's not all British actors, just the good ones.