Watson was honored for her portrayal of, Janet Leach, the appropriate adult the show is named for and West took the prize for his work as a British serial killer, The Guardian reported.
Monica Dolan, who played Rose West, Fred West's wife -- who was also a serial killer -- took home an award for best supporting actress.
The cast said the script, which paid tribute to the Wests' victims, was sensitive and avoided sensationalism.
"Of course [I had doubts], but the script answered a lot of questions about the focus of the film," said Dominic West. "I was sure that this case should be addressed and that human depravity should be addressed. The question was how you do it -- and I think we did it right."
Watson said playing Leach was difficult for her.
"By the end of it, I was so happy to flee that set," she said. "I felt I had been run over by a truck. I know things that I wish I didn't know about that case. Truly terrible depravity. Did I hate Rose West? I think it goes beyond hate. The more we studied, the more we learned, the less we understood."
Steven Moffat, a writer for BBC1's "Doctor Who" and "Sherlock," took home the Bafta TV Special award. Moffat was presented the award by Sherlock's Benedict Cumberbatch and Matt Smith, who plays Doctor Who.
"Sherlock Holmes and Doctor Who giving me an award!" exclaimed Moffat, who described the award as "the upbeat part of the obituary" and his characters as "the two best things the British have ever given to the world."
Celebrity Families of 2014 [PHOTOS]