There are two good reasons for doubting that the result of the referendum really means that the majority of the people eligible to vote want to leave the EU.
First, any vote about change has an inherent bias in favour of change. By definition, people who want change are discontented. It is easy to stir up discontent, but nearly impossible to stir up contentment: that’s just human nature. It takes an effort to go out and vote, and the discontented are far more likely to make that effort than people who are happy with the way things are. When true opinion is equally divided, a higher proportion of the discontented will vote, and there will be a majority for change.
Secondly, and far more importantly, when an unpopular government calls for a vote on anything whatsoever, there will be a bias against what that government proposes. Some people will take the opportunity to vote against the government, regardless of what they really think of the proposal. The Cameron government’s austerity program, and the haughty and heartless way they presented it, had made them extremely unpopular in some parts of the country, specially those hurt by the still-loathed Thatcher government. The Government should have remained neutral in the referendum, if it wanted a clear vote. Instead, it actively campaigned on the Remain side: and it did so in the same haughty and hectoring manner, and largely in the person of the same Chancellor, they advocated austerity. They invited a strong anti-government vote, and must surely have got it. The polls all said that Remain was bound to win anyway, so it was safe vote Leave when you didn’t really mean it.
It’s impossible to put an exact number on either of these two factors: but it is reasonable to believe that together they were more than enough to have swayed the 2% of voter decisions that gave Leave a majority. When the effects of the purely negative “campaign fear” of the Remain side and the dishonest claims of the Leave campaign are added, it becomes difficult for a reasonable person to believe that the Leave majority represented the true will of the people.