Direct democracy isn't the only form of democracy.
We're all irrational and biased, that's inherent to being human. Some people are more informed than other and there are processes to mitigate biases (direct democracy isn't one of them).
The problem comes from people who have no business in the vote, no knowledge of the issues, are not even aware of what biases are, and drink the propaganda kool aid.
Brexit was mostly about:
- "we spend to much money on EU"
- "too many migrants"
Well first off London only strives because of international financial businesses, closing the borders and making it harder for people to migrate is a death sentence [0]. Since the vote Brexit cost the UK much more than what they contribute to the EU [1], they export/import ~50% of their good to/from Europe [2]
Time will tell, what I'm convinced of is that Brexit was sold on lies. It might turns out good for them, but if it does it won't be because of good planning and well thought decisions, it'll be a combination of luck and really good damage control.
[0] https://www.ft.com/content/371c63ba-4b08-11e9-8b7f-d49067e0f...