Maybe, but I think the media's inability (as a whole) to deal with the breakdown in competency amongst the political class is a pretty direct cause of where we are now. Sure there's always been Domesday cultists working for some big papers, but its the legitimisation the BBC gave the likes of UKIP from the early days which fanned the flames that led to Brexit.
First I just have to insert the disclaimer that I think the causes of this mess are too numerous and complex and interrelated to summarise in a short post.
Having said that, my take on it would be that while I agree it is a cause of where we are now, it is only one of many, and I wouldnt personally describe it as a primary cause, or one of the main causes. The media, as in the MSM, such as the BBC, are less powerful than they used to be. If I was going to attribute this to a section of the media I would put it down to new media more than old, to social media - Facebook and Twitter. A lot more has been said about this in the social media thread and I wont go into it too much here but I will repeat something I mentioned a week or two ago in there, which was about parallels between the rise of social media and the early days of newspapers, to the first cheap, widely available daily newspapers. As they gained traction in Europe the population became increasingly radicalised, and within a couple of decades, in 1848, you can revolutions across most of Europe.
For me, when you look at the kind of upheaval we have in the UK at the moment - and in the US and loads of other places, taking different forms and different levels of severity in each place - and you are looking for a cause, you need to identify something that changed. Has MSM changed significantly? Enough to trigger all this? Its dying, you could argue, but it hasnt really changed, not fundamentally. So why would all this be happening now? What has changed is social media, not the BBC. (I dont think the competency of the political class has changed much either. Maybe things have come out confirming pre-existing concerns about their competence and integrity, such as the expenses scandal (revealed by a bastion of the UK press by the way) but I think people have been pretty cynical about their politicians for a long time.)
But I dont even think that is the main reason. I think, if you are going to put it down to one thing, it is economics. Revolutions happen when extended periods of growth and rising prosperity suddenly end. When people get used to believing that, whatever hardships they face, things will be better for them in years to come than they are now, and that their kids will be better off than them, but then that belief is eroded or killed entirely. What is bearable when average prosperity is rising is not bearable when it isnt. And that is what we have seen in the last 10-12 years. In January 2007 people had optimism about the future. By the end of 2008 they were genuinely asking themselves whether their money was safe in banks. Then austerity happened, people no longer felt financially secure and resentment about inequality went through the roof. Today it is common for people to believe things will be harder for our kids than it is for us. People fear losing their jobs, they fear automation, they fear offshoring, they fear never being able to afford a house, never being able to clear their credit card debt and the rest of it.
People were angry and in the mood to revolt. And then, along comes a referendum about the EU. In retrospect the result is completely predictable.
So does the media play a role in that? Definitely. You cant put this down to a thing and deny the input of other things, it is infinitely complex and interrelated, as I said. Has the media helped channel the anger into what it is, scapegoating immigrants and red tape as though they are the reasons they have lost their financial security? Of course it has. But ultimately I believe the shit was always going to hit the fan, one way or the other, after the crisis of 2008. Especially given the way none of the shenanigans were ever really punished, the people who caused it ended up getting richer and a system seen as grossly unfair by many was left largely intact. A few technical reforms nobody really understands about bank capital hardly feels like a satisfactory resolution to a crisis that triggered austerity.