The programme collected the best documentary series prize at the Royal Television Society Awards staged in London.
Michael Steer, a maths teacher who was a regular face on the series set in Dewsbury's Thornhill Community Academy, offered an unflattering dedication as he picked up the award.
He told guests from the TV industry: "On behalf of teachers I'd like to dedicate this award to Michael Gove and I mean dedicate in the Anglo Saxon sense which means insert roughly into the anus of."
Other winners included Stephen Fry who was named best presenter for his series Stephen Fry: Out There in which he travelled to a number of countries to examine how they treated their gay communities. The broadcaster famously made an attempt on his own life as he made the series as it left him at such a low ebb.
He paraphrased Winston Churchill to tell guests: "I think you can judge a civilisation by the way it treats its minorities."
Idris Elba took the best actor prize for his performance in BBC1 detective series Luther.
Olivia Colman won the best actress prize for the second year running for her role in Broadchurch with judges calling her "an actor at the top of her game".
Taking to the stage without her shoes, she said: "I kicked them off under the table and forgot to put them back on."
She beat Glasgow actress Sharon Rooney for her role in E4's My Mad Fat Diary.
Broadchurch won a second prize at the event hosted by comic Tim Vine by landing the best drama serial award.
Channel 4 was the biggest winner of the night sharing in nine awards for which it was the broadcaster.
Outgoing BBC2 controller Janice Hadlow was given the "judges' award" for her achievements with the channel.
Veteran actor David Suchet was honoured with the lifetime achievement award in recognition of his quarter of a century portraying Hercule Poirot.
The star was unable to attend the event after feeling unwell before the ceremony.
Coronation Street took the best soap prize.
Here are the winners in full:
Olivia Colman - Broadchurch (ITV)/Run (Channel 4)
Idris Elba - Luther (BBC1)
Imagine...Vivian Maier: Who Took Nanny's Pictures (BBC1)
:: Children's Fiction
Dumping Ground (CBBC)
:: Children's Programme
Hard Times - A Newsround Special (CBBC)
:: Comedy Performance
Brendan O'Carroll - Mrs Brown's Boys (BBC1)
Four Rooms (Channel 4)
:: Documentary Series
Educating Yorkshire (Channel 4)
:: Drama Serial
:: Drama Series
Peaky Blinders (BBC2)
The Last Leg (Channel 4)
:: Entertainment Performance
Alan Carr - Alan Carr: Chatty Man (Channel 4)
Richard III: King In The Car Park (Channel 4)
Game Of Thrones (Sky Atlantic)
:: Live Event
The Ashes - 2013 (Sky Sports)
:: Popular, Factual and Features
Gogglebox (Channel 4)
Stephen Fry - Stephen Fry: Out There (BBC2)
:: Science and Natural History
:: Scripted Comedy
:: Single Documentary
The Murder Trial (Channel 4)
:: Single Drama
The Challenger (BBC2)
:: Soap and Continuing Drama
Coronation Street (ITV)
:: Sports Presenter, Commentator or Pundit
Gary Neville - Sky Sports (Sky Sports)
:: Sports Programme
World Athletics - Mo Farah's Double Gold Win (BBC1)
:: Comedy Writer
James Corden, Mathew Baynton and Tom Basden - The Wrong Mans (BBC2)
:: Drama Writer
Marlon Smith and Daniel Fajemisin-Duncan - Run (Channel 4)
:: Judges' Award
:: Lifetime Achievement