Sian Clifford was in tears when she realised she had won the Bafta for Female Performance In A Comedy Programme over her Fleabag co-star Phoebe Waller-Bridge.
In her acceptance speech Clifford, who played Claire on the hit comedy show, said she didn't "believe in competition" and that "there's no Claire without Fleabag".
This year's ceremony was broadcast as live on BBC One from behind closed doors due to the coronavirus pandemic, with nominees accepting their awards virtually.
The Leading Actor award went to Jared Harris for his part in Sky Atlantic drama Chernobyl, while the show also came out top in the best mini-series category.
Speaking from his home via video link, he said: "Wow, that's a surprise. BAFTA, you've ruined my losing streak! I'm annoyed at you.
"You know ... this show has won a lot of accolades and I think that's testament to [producers] Craig Mazin and Carolyn Strauss and Jane Featherstone's stewardship. I'd say the best decision they made was to put every single episode in [director] Johan Renck's hands. He's a bada**."
Glenda Jackson beat off stiff competition from Jodie Comer (Killing Eve), Suranne Jones (Gentleman Jack) and Samantha Morton (I Am Kirsty) in the Leading Actress category. She was awarded the Bafta for her portrayal of Maud Horsham in Elizabeth Is Missing.
Idris Elba was awarded the Bafta Special Award. In his speech, he said that in the future he hoped to pick up a Bafta for his acting abilities.
He said: "I feel I want to write a lot more and direct a lot more, I've been producing for about five years.
"You plant your seeds and cultivate your land, and it comes up really slowly, I would like to win a Bafta as an actor one day."
He also spoke about the struggles he has faced in his career, saying: "There is always hard times, I've definitely seen my fair share of them, definitely in the late 90s was a real struggle for me as an actor but it was that struggle that got me prepared for the next stage of my career when The Wire took off."
The Must-See Moment Award, which is voted for by the public, went to Gavin And Stacey for the scene in which Nessa proposes to Smithy from the BBC show's recent Christmas special.
Co-creator Ruth Jones said: "Thank you to everybody who was involved in making the show. It was really joyous experience for us all. Winning this Bafta is immense."
Fellow co-creator James Corden added: "This is the lovely icing on an already really lovely cake. Ruth, any other cake references you would like to add?"
Jones replied: "I just want to sink my teeth into that Bafta and suck all the sugary juices from it."
In the Soap & Continuing Drama category, the Bafta was awarded to Emmerdale while Strictly Come Dancing nabbed the Entertainment Programme award for the second time in its 16 year history. Head judge Shirley Ballas thanked the celebrities who "throw themselves into the world of Strictly".
Other winners on the night included Mo Gilligan with Best Entertainment Performance for The Lateish Show With Mo Gilligan, while Race Across The World was named winner of the Reality and Constructed Factual.
The Bafta TV award for Comedy Entertainment Programme went to Taskmaster, which airs on Dave.
Some winners recorded their acceptance speeches in advance not knowing whether they had won or not, while others appeared via video call.
Tim Minchin opened the first-ever socially-distanced Bafta TV Awards with a song he wrote especially for the event.
'𝘛𝘰 𝘢𝘭𝘭 𝘺𝘰𝘶 𝘤𝘭𝘦𝘷𝘦𝘳 𝘯𝘰𝘮𝘪𝘯𝘦𝘦𝘴, 𝘐 𝘩𝘰𝘱𝘦 𝘺𝘰𝘶'𝘳𝘦 𝘷𝘦𝘳𝘺 𝘷𝘦𝘳𝘺 𝘱𝘭𝘦𝘢𝘴𝘦𝘥. 𝘐’𝘮 𝘯𝘰𝘵 𝘣𝘪𝘵𝘵𝘦𝘳 𝘵𝘩𝘢𝘵 𝘮𝘺 𝘴𝘩𝘰𝘸 𝘸𝘢𝘴𝘯’𝘵 𝘯𝘰𝘮𝘪𝘯𝘢𝘵𝘦𝘥'@TimMinchin opens the #VirginMediaBAFTAs with an epic anthem for the times! pic.twitter.com/ktRBljNfgH— BAFTA (@BAFTA) July 31, 2020
The Bafta TV awards were due to take place on May 17, while the craft awards, which celebrate technical achievements, were to be held on April 26, but were postponed because of the coronavirus crisis.
TV Baftas 2020 winners:
Jodie Comer, Killing Eve - BBC One
Glenda Jackson, Elizabeth is Missing - BBC One - WINNER
Suranne Jones, Gentleman Jack - BBC One
Samantha Morton, I Am Kirsty - Channel 4
Stephen Graham, The Virtues - Channel 4
Jared Harris, Chernobyl - Sky Atlantic - WINNER
Takehiro Hira, Giri/Haji - BBC Two
Callum Turner, The Capture - BBC One
Naomi Ackie, The End of the F***ing World - Channel 4 - WINNER
Helen Behan, The Virtues - Channel 4
Helena Bonham Carter, The Crown - Netflix
Jasmine Jobson, Top Boy - Netflix
Joe Absolom, A Confession - ITV
Josh O'Connor, The Crown - Netflix
Will Sharpe, Giri/Haji - BBC Two - WINNER
Stellan Skarsgard, Chernobyl - Sky Atlantic
Frankie Boyle, Frankie Boyle's New World Order - BBC Two
Mo Gilligan, The Lateish Show with Mo Gilligan - Channel 4 WINNER
Lee Mack, Would I Lie to You - BBC One
Graham Norton, The Graham Norton Show - BBC One
Male performance in a comedy programme
Jamie Demetriou, Stath Lets Flats - Channel 4 - WINNER
Ncuti Gatwa, Sex Education - Netflix
Youssef Kerkour, Home - Channel 4
Guz Khan, Man Like Mobeen - BBC Three
Female performance in a comedy programme
Sian Clifford, Fleabag - BBC Three - WINNER
Gbemisola Ikumelo, Famalam - BBC Three
Sarah Kendall, Frayed - Sky One
Phoebe Waller-Bridge, Fleabag - BBC Three
The Crown - Netflix
The End Of The F***Ing World - Channel 4 - WINNER
Gentleman Jack - BBC One
Giri/Haji - BBC Two
Brexit: The Uncivil War - Channel 4
Elizabeth Is Missing - BBC One
The Left Behind - BBC Three - WINNER
Responsible Child - BBC Two
A Confession - ITV
Chernobyl - Sky Atlantic - WINNER
The Victim - BBC One
The Virtues - Channel 4
Soap and continuing drama
Casualty - BBC One
Coronation Street - ITV
Emmerdale - ITV - WINNER
Holby City - BBC One
Euphoria - Sky Atlantic
Succession - Sky Atlantic
Unbelievable - Netflix
When They See Us - Netflix - WINNER
The Greatest Dancer - BBC One
The Rap Game UK - BBC Three
Strictly Come Dancing - BBC One - WINNER
The Voice UK - ITV
Comedy entertainment programme
The Graham Norton Show - BBC One
The Last Leg - Channel 4
The Ranganation - BBC Two
Taskmaster - Dave - WINNER
Catastrophe - Channel 4
Derry Girls - Channel 4
Fleabag - BBC Three
Stath Lets Flats - Channel 4 - WINNER
Joe Lycett's Got Your Back - Channel 4
The Misadventures Of Romesh Ranganathan - BBC Two - WINNER
Mortimer & Whitehouse: Gone Fishing - BBC Two
Snackmasters - Channel 4
Coronation Street, the death of Sinead Osborne - ITV
Fleabag, Confessional scene - BBC Three
Game of Thrones, Arya kills the Night King - Sky Atlantic
Gavin and Stacey, Nessa proposes to Smithy - BBC One - WINNER
Line of Duty, John Corbett's death - BBC One
Love Island, Michael recouples after Casa Amor - ITV2
Growing up Poor: Britain's Breadline Kids (Dispatches) - Channel 4
The Hunt for Jihadi John - Channel 4
Is Labour Anti-Semitic? (Panorama) - BBC One
Undercover: Inside China's Digital Gulag (Exposure) - ITV - WINNER
The Abused - Channel 5
David Harewood: Psychosis And Me - BBC Two
The Family Secret - Channel 4
The Last Survivors - BBC Two - WINNER
Crime and Punishment - Channel 4
Don't F**K With Cats: Hunting An Internet Killer - Netflix
Leaving Neverland - Channel 4 - WINNER
Our Dementia Choir With Vicky McClure - BBC One
Reality and constructed factual
Celebrity Gogglebox - Channel 4
Harry's Heroes: The Full English - ITV
Race Across The World - BBC Two - WINNER
RuPaul's Drag Race UK - BBC Three
8 Days: To The Moon And Back - BBC Two
Seven Worlds, One Planet - BBC One
Thatcher: A Very British Revolution - BBC Two
Yorkshire Ripper Files: A Very British Crime Story - BBC Four - WINNER
Hong Kong Protests - Sky News - WINNER
ITV News At Ten: Election Results - ITN/ITV
Prince Andrew & The Epstein Scandal (Newsnight) - BBC News/BBC Two
Victoria Derbyshire: Men Who Lost Loved Ones To Knife Crime - BBC News/BBC Two
2019 Rugby World Cup Final: England v South Africa - ITV - WINNER
ICC Cricket World Cup Final - Sky Sports Cricket
Fifa Women's World Cup 2019 Semi Final: England v USA - BBC One
Wimbledon 2019 Men's Final - BBC One
Blue Planet Live - BBC One - WINNER
Election 2019 Live: The Results - ITN/ITV
Glastonbury 2019 - BBC Two
Operation Live - Channel 5
Anywhere But Westminster - The Guardian
Brain In Gear - BBC iPlayer - WINNER
Soon Gone: A Windrush Chronicle - BBC Four
Toni_With_An_I (Born Digital: First Cuts) - BBC Four