Those percentages aren't even correct for the entire population cause not everyone voted. And I would argue most people that didn't vote just wanted it to stay same as, and didn't think Leave would've polled so highly among the voters.

The problem is that it was an advisory vote

This is sometimes raised, but is misleading. The only reason it was legally advisory is because in the British system of government, the UK cannot bind Parliament; the House of Commons can override anything else.

In the system of government in some countries, the option for a meaningful legal difference between two types of referendum exists.

The British government had been explicit that what the British public voted for would be implemented; this is the closest analog to a binding referendum. Had they simply wanted to request the advice of the public, it would have been announced that they would take the outcome under consideration.

This is not to say that having that referendum was s good idea. It is just to say that the binding/advisory nature is really a property of the British system of government, not to indicate that the intent was to merely take the public's vote as advice.

Nigel Farage was already gearing up to become a massive thorn in everyone's backside. He actually thought it probably would go that way he didn't realize that he barely won.

"Which is the best brand of brown sauce?"

Yup, you're a real hero with your populism. Look how great that turned out.

People these days treat democracy like a damned religion instead of a system of governance. Turns out though that complex decisions often benefit from expertise instead of letting the lowest common denominator decide.

They were, in who they elect to represent them.