Not being heavily involved in politics, national or international, I only got the occasional FB post or news article that even clued me in that the referendum was pending. And without exception, it was framed as "some bigots are trying to break away from the EU, but they won't have enough votes, so I don't really care". It was met from the anti side with, apparently nothing but scorn and flippant dismissal, they just couldn't bring themselves to even entertain the thought it might pass, so they prepared no counterpoint... at least that's how it looked to me.
First rule of politics: Run scared, or don't run.