Once Upon a Time in Northern Ireland was among the winners at the BAFTA Television Awards in London earlier this year.
It was made by Keo Films and Walk on Air Films for BBC Two and BBC Northern Ireland.
Also at the Edinburgh ceremony, Graham Norton won the Best TV Presenter - Entertainment award.
BBC's The Traitors picked up the Best Entertainment Series award for the second year running.
ITV1 was named Channel of the Year.
The ITV drama Mr Bates Vs The Post Office, which sparked a national conversation in the UK about the Horizon IT scandal, won two awards.
The four-part series, which dramatised the wrongful prosecution of Post Office workers, took home Best Drama.
One of its stars, Monica Dolan, was named Best TV Actor - Drama for her role as the wrongly accused former sub-postmaster Jo Hamilton.
The team behind the series dedicated it to campaigner Alan Bates and all those caught up in one of the biggest miscarriage of justice scandals in the UK.
The BBC festive programme Hairy Bikers - Coming Home for Christmas won the TV Moment of the Year award, which is the only prize to be voted for at the Edinburgh TV Festival by the public.
One half of the biking and cooking team, Dave Myers, died earlier this year at the age of 66 following a battle with cancer.
Channel 4 collected the award for Best Comedy Series for Big Boys.
Bridget Christie was named Best TV Actor - Comedy for her performance in Channel 4's menopause show The Change.
The Breakthrough Performance Award went to Dylan Thomas-Smith for his performance in the ITV sitcom G'wed.
The Booker Prize-shortlisted author Nadifa Mohamed was named Best Presenter - Factual for the Channel 4 historical documentary Britain's Human Zoos.
The BBC's Sort Your Life Out won the award for Best Popular Factual Series.
Studio Lambert, which makes the BBC shows The Traitors and Race Across the World as well as the Netflix series Squid Game: The Challenge, was named Production Company of the Year.
The Climate Impact Award went to The Great Climate Fight, which was screened on Channel 4.
The Small Indie of the Year award went to the production company Hardcash, which worked on the documentary Russell Brand: In Plain Sight.
Big Brother producer Banijay UK was named Production Group of the Year.
The Outstanding Achievement award, which was previously announced, went to consumer rights champion Martin Lewis.
Additional Reporting: Press Association
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