I’d actually argue that fear-mongering writing did cause Brexit — Boris Johnson was fired from the…
Jamie Pohotsky
1

As much as I execrate Boris, I am not sure I could single-handedly blame Brexit on him. Brexit is a statement of the fact that the EU is not working for 52% people, and those 52% did not vote Leave just because Boris told them to… He is about as trusted as a midnight shopping channel. The problem with framing it as a fear-response is that if people fear something, normally they vote to preserve the status-quo, so they would have voted Remain. In my opinion, Stratfor ran a particularly good narrative of what Brexit is the symptom of, but it’s rather more complex and can’t be reduced to a single factor:

https://www.stratfor.com/weekly/making-sense-brexit