The event recognises the most talented small screen stars, with Sophie receiving her Best female actor gong for series Undercover and Robbie taking home the Best male actor prize for the gripping drama National Treasure. The programme, which told the story of a public figure accused of multiple sexual assaults, was also awarded the Mini-Series prize, while Robbie's co-star Julie Walters was honoured with a lifetime achievement award.
Joking the prize was an "old people's award", Julie told the audience: "It's absolutely gorgeous, I'm thrilled. I always get excited at things like this, being surrounded by people I know, I'm like a Jack Russell dog."
Television presenting pair Ant and Dec picked up the Best entertainment show prize for Saturday Night Takeaway, and told the crowd Adele is next on their dream guest list for the programme.
"We've never quite made it work because of all her tours and albums and stuff, but we could have a lot of fun with her," they said. "If you all put the pressure on from your end and we put the pressure on from our end, maybe we can make it happen."
Grayson Perry was another big winner on the evening, taking home both the Arts gong and the Presenter prize for his show Grayson Perry: All Man, which saw him look at the modern idea of masculinity.
Speaking about the programme, Grayson explained: "The conversations I had with people on the streets are really what we want to be talking about now and that's why I feel like I'm doing the right thing.
"Good television should have that water cooler effect of starting conversations - I have had taxi drivers talk to me about it and that's lovely. It's not my day job so I feel pretty good that I've just wandered unexpectedly into television and we've struck a nerve."
Meanwhile, Emmerdale beat its competitors to take home the Soap and continuing prize gong, with producer Iain MACLeod commenting the award represented the ITV show being given "the recognition it deserves".
The RTS Awards were hosted by Sandi Toksvig, who was recently announced as one of the new presenters of The Great British Bake Off.
The full list of winners at the 2017 RTS Awards is as follows:
Best female actor: Sophie Okonedo - Undercover
Best male actor: Robbie Coltrane - National Treasure
Arts: Grayson Perry - All Man
Breakthrough: Phoebe Waller-Bridge - Fleabag
Children's programme: CBeebies - A Midsummer Night's Dream
Comedy performance: Asim Chaudhry - People Just Do Nothing
Daytime programme: Find it, Fix it, Flog it
Documentary series Exodus: Our Journey to Europe
Drama series: Happy Valley
Entertainment: Ant and Dec's Saturday Night Takeaway
Entertainment performance: Adam Hills, Alex Brooker and Josh Widdicombe - The Last Leg
History: The Aberfan Young Wives' Club
Live Event - Stand Up to Cancer
Mini-Series: National Treasure - The Forge
Presenter: Grayson Perry - Grayson Perry All Man
Popular factual and features - Employable Me
Channel of the Year: BBC Three
Science and natural history: First Contact: Lost Tribe of the Amazon
Scripted comedy: People Just Do Nothing
Single documentary: The Murder of Sadie Hartley
Single drama: Murdered By My Father
Soap and continuing drama: Emmerdale
Sports presenter, Commentator or Pundit: Osi Umenyiora
Sports programme: Rio Paralympics Sunset
Best comedy writer: Phoebe Waller-Bridge - Fleabag
Best drama writer: Sally Wainwright - Happy Valley
Judges' award: Sally Wainwright
Lifetime achievement award: Julie Walters
With an ingenious concept, this fairly simple film becomes one of the most gripping thrillers...
Nine people from different walks of life who all work for the government are enlisted...
Cypher Raige is a renowned military general who finds himself and his frightened 13-year-old son...
Based on a true story, his powerful drama tells an important story from Apartheid-era South...
Watch the trailer for The Secret Life Of BeesThe Secret Life Of Bees is based...
Caucasians, apparently, have no soul. Or heart. Or common sense. According to the movies, whenever...
Scenes Of A Sexual Nature Trailer First time British director Ed Blum presents Scenes of...
This summer sees the eagerly awaited big screen debut of 14 year old special agent...
The title of Stephen Frears' new film Dirty Pretty Things revels in contradiction. The same...