The ITV1 show, Appropriate Adult, picked up the Leading Actor, Leading Actress and Supporting Actress awards for three of its stars.
Leading Actor winner Dominic West paid tribute to Janet Leach who was the appropriate adult of the title and acted as Fred West's confidante after his arrest.
He said: “I hope she has had some closure and we have honoured the suffering she endured and the suffering of all the West's victims, living and dead.”
Leading Actress winner Emily Watson also paid tribute to Leach, who she portrayed, and admitted she was worried when she first heard about the attempt to make a show about a story of such “truly terrible depravity”.
She said: “When I first heard about this show I thought I probably shouldn't do it because of the subject matter - and then I read the script.”
But she admitted the role had taken its toll, saying: “I know things I wish I didn't about that case.”
Monica Dolan won the Supporting Actress gong for her portrayal of Rose West and said the role had been “a privilege”.
She paid tribute to the West's victims, many of whom were never reported missing, saying: “I'd love to live in a world where everyone was missed.”
Other big awards included the gong for Supporting Actor which went to Andrew Scott who played the villainous Moriarty in Sherlock.
Scott, who beat his co-star Martin Freeman to pick up the award, thanked his mum and dad and paid tribute to the “exceptionally talented Mr Benedict Cumberbatch”, who plays Sherlock Holmes.
Speaking backstage, he said he had not watched earlier versions of Moriarty.
He said: “I just tried to look at what's dark within my own self.”
The Special Award went to the show's co-writer Steven Moffat, who also writes Doctor Who.
It was presented to him by the shows' two stars, Benedict Cumberbatch and Matt Smith.
Sherlock actor Cumberbatch described Moffat as “a word machine” and said “his name is a byword for quality family entertainment”, while Doctor Who star Smith described the writer as “brilliantly cantankerous”.
Accepting the award, the Scot said he owed a great deal to “the two best things the British have ever given to the world: Sherlock Holmes and Doctor Who”.
Last night's event, which is formally known as the Arqiva British Academy Television Awards, was hosted by comedian Dara O'Briain at the Royal Festival Hall.
The Irish comic lost out on the award for Entertainment Performance which went to Graham Norton.
O'Briain joked he could not begrudge the Eurovision Song Contest coverage host his award “because he's spent the last 24 hours comforting Engelbert Humperdinck”.
The award for Drama Series went to BBC3 show The Fades which was cancelled recently by the corporation.
Scriptwriter Jack Thorne said he was “amazed and shocked”, and put his success down to the “lucky socks” he was wearing.
The Single Documentary award went to BBC2's Terry Pratchett: Choosing To Die - the best-selling author's examination of euthanasia.
Pratchett, who has been diagnosed with Alzheimer's, thanked the BBC for “allowing us to tackle this rather strange subject for a documentary”.
He also paid tribute to the family of Peter Smedley who allowed the documentary film to show his final days in the run-up to his death at a clinic.
Pratchett said: “It turned us about a bit but we saw what happened and so did you.”
The award for Single Drama went to Channel 4's Random and the Current Affairs gong was given to BBC1's Panorama: Undercover Care - The Abuse Exposed.
The Factual Series award went to BBC3's Our War which followed British troops on the ground in Afghanistan.
BBC1's Mrs Brown's Boys won the Situation Comedy category, beating competition including Rev and Fresh Meat.
Its star Brendan O'Carroll said: “All we wanted to do was make people laugh and it seems to have worked.”
The International Award went to the critically-acclaimed Danish political drama Borgen.
Coronation Street scooped the award for Soap and Continuing Drama.
Bill Roache, who plays Ken Barlow, accepted the award and praised the “team effort” behind the long-running show.
Olympians Dame Kelly Holmes and Jonathan Edwards presented the award for Sport and Live Event to the team behind BBC1's coverage of the Royal Wedding.
The Specialist Factual award went to Channel 4's Mummifying Alan: Egypt's Last Secret.
The show illustrated how the ancient Egyptians mummified bodies by using the corpse of a recently deceased Torquay taxi driver, Alan Billis.
The Mini Series award went to Shane Meadows' This Is England '88, with the writer and director thanking his real family and his “film family”.
The best Entertainment Programme award went to Derren Brown: The Experiments.
Jennifer Saunders won the award for Female Performance in a Comedy Programme for her return to Absolutely Fabulous.
The star said: “That was a bit of a shock, thank you for still finding it funny.”
The YouTube Audience Award, the only one voted for by the public, went to Celebrity Juice - the quiz show hosted by Keith Lemon, the comic alter-ego of Leigh Francis.
The award for best Male Performance in a Comedy Programme went to Darren Boyd for Sky One's Spy.
Having beaten better-known names including Hugh Bonneville and Tom Hollander, Boyd promptly said he should never have won, adding: “This is ridiculous, but I'll take it.”
The last award of the night was the Bafta Fellowship, given to veteran Australian artist and entertainer Rolf Harris.
The star, who described himself as “humbled”, said: “How amazing is it to discover what you love doing most can become your career, if you've been as lucky as I have been.”