Only 7% of the country voted on the basis of issues related directly to the EU.
Leave themselves have said they based their strategy not on a cohesive idea of what Brexit was but more on a variety of issues where there was political dissatifaction. They decided to leave the concept of Brexit to the imagination of Leave Voters rather than define it.
Therefore you had a bunch of people voting for Brexit because they didn't like Cameron and Osborne and were making a protest vote about austerity, or because they want to join the Euro, another bunch because they don't like immigration, another group because they were pissed off about potholes and bins not being emptied (I'm not actually joking - this was what was found in surveys afterwards!), another group because they don't like the ECHR, another group because they wanted financial liberalisation and to get rid of workers rights etc etc. But nothing whatsoever which was ultimately unified in its thinking and logic.
To say it was a majority idea is as misleading as suggesting a minority voted for it. That was precisely May (and later Johnson's) problem - they couldn't get a clear majority for what Brexit should ultimately be - because the vote was so fractured between interest groups and what they thought Brexit should be because it had been left to be 'in the eye of the beholder'.
It was THE catastrophic error by the Tory Party - because it meant that NONE of the arguments that the Referendum were supposed to resolved internally COULD be because it set up years of debate and arguments about what Brexit should be.
And thats why we are in the mess we are in.
The Leave campaign was successful only at winning a vote. It was not successful in identifying and defining what Brexit was / should be - by design. The referendum was therefore nothing but an exercise in how to win an electoral campaign. What it wasn't was a cohesive political movement which represented a majority within British politics nor the British public.
Understanding the difference is essential to understanding anything about British politics in the last 10 years - this is totally regardless of your political leanings either party political or with regards to Europe.