Apart from answering with the cliched stuff (Iraq and the corporate media's role in pushing it, Chomsky's book on the whole thing), well before the rise of independent media, people in the UK believed that the number of people on benefits was much higher than it was, the benefits they received were much higher than the reality, and the number of incoming migrants and of Muslims was much higher than it was. This was from a rich diet of corporate media. I could
find a related link from 2016, but remember similar stories in the early 2010s, and probably it was an ongoing thing then too.
Another slightly less cliched criticism of the msm (BBC in particular) is this guy's columns about the role of lobbyists and PR in media that is taken as impartial. I could find a few links:
https://www.monbiot.com/2013/12/12/puppet-show/
https://www.monbiot.com/2014/07/01/purging-dissent/