There used to be a lot of media coverage on BBC2 and Channel 4, both very different channels in the 1990s. Some features from arts programmes like The Late Show, specials and regular programmes on the media that spring to mind:
Did You See? (BBC2)
The Late Show (BBC2)
TV Hell Night (BBC2)
One of BBC2's best theme nights in the 1990s. Here's one programme on TV-AM. Others on YouTube include the A-Z Of Hell, Disastermind and Hello and Goodbye.
Trouble At The Top - Nightmare At Canary Wharf (BBC2)
Behind the scenes of the launch of Live TV by Janet Street-Porter and Kelvin Mackenzie:
Watch This Or The Dog Dies - The History Of Youth TV (BBC2)
The Media Show (Channel 4)
Right To Reply (Channel 4)
There was also a big season on TV news on Channel 4 in the 1990s "Whose News" which included this edition of its polemic strand "J'Accuse".
I can't find any clips on YouTube but there was a weekly media show "Late Media" on BBC2 in the 1990s, presented by Joanna Coles who used to present Mediumwave on Radio 4.