Brexit was just another item in the long list of why representative democracy is a terrible idea. Ordinary people know nothing and understand even less. Asking them their "opinion" about anything is not merely a waste of time but, as Brexit, Trump, Modi, Erdogan, Bolsonaro, Duterte, et al demonstrate clearly, a one-way street to catastrophe. Brexit was always predictably going to be a monumental example of unnecessary self-harm, but it occurred because ordinary people don't know enough not to cut off their own legs. There will be countless more Brexit-like events on scales large and small until everything we valued has been corroded away. After that, who knows how many years or centuries of darkness before - one must hope - a small group of clever people are able to organize and construct a far better approach to governance.
Until then, Brexit is merely one of many warm-up acts. Much worse is to come because ordinary people will reliably vote for self-harm every time they're given the chance, because self-harm will always be dressed up in easy-to-remember soundbites by cynical demagogues and there's nothing more powerful for capturing the limited intellects of ordinary people than an easy-to-chant soundbite.