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But after these fine actors are trained, the work available to them at home is limited.

“As an actor, you have to travel where the work is, so here I am,” said Sophia Myles, who plays the love interest of the lead vampire (played by an Aussie) in “Moonlight.”

“In England at the moment our government isn’t putting any money into the film business,” Miss Myles said. “We don’t really have an industry in England anymore. And American television, especially in the last few years, is on a par, if not better than, a lot of movies out there.”

Even as American TV studios fling their casting nets wider, actors crossing the pond tend to downplay the migration. They insist the best person wins the audition, regardless of nationality.

“There’s no fast-track portal at LAX with all these British actors,” Mr. McKidd said. “It’s just coincidence.”

And they downplay their hard-won ability to sound like Americans. Mr. Lewis says he indulges in a couple of quick dialect lessons before each episode begins filming, but he mainly listens to the American actors who surround him.

Viewers seem to have no trouble accepting foreign actors in American roles. The stars of Showtime’s “Brotherhood,” Brit Jason Isaacs and Aussie Jason Clarke, play Irish Americans in Rhode Island and have been welcomed with open arms in Providence. Isaacs plays a gangster and Mr. Clarke plays a politician, both with thick New England accents.

“I was worried about how I would be received when we went back to film the second season, but it was like Norm walking into Cheers,” Mr. Isaacs (the bad brother) said. “Irish Americans in Providence are delirious about the show.”

And Mr. Clarke (the good brother) marched with the mayor of Providence in the city’s July Fourth parade.

The swarm of outsiders is so believably American that no one knows the difference — except maybe the American actors they beat out for the roles.