Game of Thrones saw off heavyweight competition to win the prize for outstanding drama series, beating the likes of The Crown, Stranger Things, The Handmaid’s Tale and Westworld.
Peter Dinklage, one of the stars of the fantasy drama, was also named best supporting actor in a drama series for his role as Tyrion Lannister.
Foy scooped the award for best lead actress in a drama series for her portrayal of the Queen on Netflix show The Crown.
She dedicated the prize to her co-star Matt Smith and the drama’s new cast, including Olivia Colman who replaces her in the forthcoming third series.
“I had the most extraordinary two and a half years of my life,” Foy said on stage.
Newton won the Emmy for best supporting actress in a drama series for her role on Sky Atlantic’s sci-fi western Westworld.
Collecting her prize, Newton said: “I don’t even believe in God but I’m going to thank her tonight.”
Other British winners included comedian John Oliver, whose show Last Week Tonight won the prize for outstanding variety talk series.
Reading-born Charlie Brooker took home the Emmy for best writing for a limited series, movie or dramatic special for his work on Black Mirror with co-writer William Bridges.
And Welsh actor Matthew Rhys collected the gong for best lead actor in a drama series for his role in The Americans.
Another notable winner was former Happy Days star Henry Winkler, who won an Emmy 42 years after he was first nominated.
The veteran actor, 72, collected the prize for outstanding supporting actor in a comedy series for his role as acting coach Gene Cousineau in HBO’s Barry.
“I only have 30 seconds but I wrote this 40 years ago,” Winkler said during his acceptance speech.
He told the audience he was once told that if you stay at the table long enough “the chips come to you”, adding: “Tonight I got to clear the table.”
It was the sixth time that Winkler had been nominated for an Emmy, including three nods for his portrayal of Arthur “the Fonz” Fonzarelli on Happy Days in the 1970s.
One of the most memorable moments of the night came when a director stunned the audience by proposing to his girlfriend on stage.
Glenn Weiss popped the question to his girlfriend Jan Svendsen after winning the award for outstanding directing for a variety special for The Oscars.
The audience erupted into loud cheers after she agreed to marry him and the camera panned on to crowd members wiping tears from their eyes.
The 70th Primetime Emmy Awards, co-hosted by comedians Colin Jost and Michael Che, were handed out live from the Microsoft Theatre in Los Angeles.