ITV's early evening news on the day of the massacre was among items found to be intrusive of relatives' grief.
"No relatives had been interviewed but the council was troubled by the length and detail of the coverage of families waiting for news ... at the information centre. Shots were used of clearly identifiable families together with the sound of their cries of anguish ... and the name of one of the victims was plainly audible. The council felt this was an unnecessary intrusion."
The BSC also upheld a complaint about the "insensitive" coverage of the killings by Capital Radio on the same day.
It felt that the presentation of The Way It Is magazine programme was "insufficiently sensitive and failed to respond adequately to the unique nature of the tragedy, although it recognised that the show had been toned down."
Also upheld were eight complaints about ITV's News At Ten on the day that the tragedy occurred. The council agreed with viewers who argued that an interview with Agnes Hamilton, the mother of the murderer, was found to be intrusive and exploited her vulnerability as a victim.
Two complaints about Channel 4 - concerning a documentary on acquiring guns illegally and a promotion showing a presenter apparently firing into the screen - were also upheld.
The BSC noted, however, that "the sensitive tone of most of the coverage, and the attempt to report what was happening in as measured and sympathetic way as possible, was underlined by the relatively small number of complaints".
It dismissed other objections, including one from a viewer who felt ITN had attempted to put "deeply shocked people on camera" on the day of the tragedy, and another who argued that BBC1's One O' Clock News had harassed a "deeply shaken" Chief Constable for more details.