The two shows picked up the Best Drama and Best Comedy honors at the O2 Arena, while British TV favorites Ant McPartlin and Declan Donnelly collected the Best TV Presenter prize for a 20th time.
Beating out "Sex Education", "The Vicar of Dibley" and "Friday Night Dinner" for the top British TV comedy gong, Gervais accepted the award and thanked Netflix bosses "for all their support and their total lack of interference," insisting, "They are just the best broadcaster."
Gervais also thanked "the amazing crew and cast, and the people at home who voted for it," adding, "You are the reason I do this... The money is... You are the second... I do it for the money and thank you."
Backstage, Ricky confessed he's still shocked by the show's popularity, telling reporters, "It's a show about a man who wants to kill himself and his wife dies of cancer, and people go, 'OK, this sounds funny.' "
Meanwhile, McPartlin and Donnelly were overwhelmed by their win. When accepting the honor, the former said, "This one means the most. Twenty years. This is really, really special. You have no idea how special this is." His hosting partner added, "It's pretty overwhelming to be honest with you."
"So much has changed in both of our lives since 2001, but one thing that hasn't changed is how unbelievably grateful we are that you take time, year after year, to vote for us and put us up here," Donnelly elaborated. "We are so honored and humbled and grateful. It means the absolute world."
There were also wins for hit reality TV show "Gogglebox", long-running soap series "Coronation Street", "The Great British Bake Off" and AIDS drama "It's a Sin".
The full list of winners is: