For the longest time, I thought this guy was a Brit

He does. He looks like an actor from the golden era, that I think makes a lot of people think he's English.

You're not the only one, this is from an interview with ScreenCrush:

I: I conducted an informal poll of five people, asking where they thought you were from. Three said “England”; one said “Scotland”; and one said “Nebraska,” which is at least closer to true.

L: [Laughs] England and Scotland?

I: People are under the impression that you are from the United Kingdom.

L: I’ve gotten that. I’ve heard that before. I don’t understand where that comes from, actually. Well, I grew up in the Middle East. My folks have a very thick, kind of Oklahoma accent, that’s where I was born. But we moved to the Middle East right after I was born, so I guess we were surrounded by English people and French people. Who knows?

I: I think ‘The Hobbit’ movies play a role, not that Thranduil is British.

L: Yeah, probably. That’s cool, though. I’ll take it.

I: I’ve heard people say, “Lee Pace’s American accent on ‘Halt and Catch Fire’ is amazing.”

L: [Laughing] Are you kidding? That’s genius. I guess I’ve played English a few times; I’ve done a couple of movies. I did ‘Miss Pettigrew Lives for a Day,’ which was English. And I did a movie called ‘Ceremony’ where I was English in that movie as well.

I: People think of you as regal.

L: I’ll take it. If it makes Peter Jackson cast me in his movies, I’ll take it.


http://screencrush.com/lee-pace-interview-the-hobbit/

Well Lee does have a lot of British in him. And look who has almost the same sort of ancestry? They even have some facial similarities. haha!

Lee Pace - He is of German, as well as English, Scottish, and Welsh, descent.

Tom Hiddleston - His father is Scottish. His mother is English, and has English, Welsh, and German ancestry. One of Tom's maternal great-great-grandfathers was of German origin.

OK...to me Lee and Tom look nothing like each other.

Come on, he was born in Chickasha, OK. 

Right, and he sounds and behaves when not in character very American to me. But I know many people are or have been under the impression he was British. That's interesting.

Did he play a Brit in something? Maybe that's why, because other than that, I don't know what evidence anyone has he is from the UK?

Yes he played a British man in 2 different movies, perhaps people saw those first and thought he'd be British.