I'm really not sure how a lot of the wishes of the 52% can be delivered, you're right about not all of it being related to the EU.
The elites narative that was peddled by the leave campaign certainly appealed to some, especially those in areas which have experienced deindustrialisation and have suffered economically because of it.
My own experience of this is being from the North East ( despite now living in London) and discussing the issue with family and friends up there. It really annoys leavers when you disucss this, alongside the documentaries made by the BBC/Sky etc which sought to find out their reasons for leaving, but most really weren't about the EU at all.
There is a lot of anger about austerity, which has had major impacts in the North East where government agencies are among the biggest employers, there have been redundancies, pay cuts and freezes etc and declining public services. There have been big cuts to bus services, isolating people along with many other cuts to services which had previously been seen as essential.
There is a feeling of abandonment and much anger that "That London" gets far more public spending on it. A friend of mine was spitting blood when it was revealed the the per capita spend on subsidising public transport and infrastructure in London was £2,500 but it County Durham it was £5.
There are also negative feelings regarding immigration, which has taken some of the blame for probems caused by austerity. There was also fear stoked about immigration and Turkey, as well as preying on people's fears regarding public services and immigration.
The leave campaign did appeal to many people, for a myriad of reasons but the increased spending on public services was one.
Here is my real key point though, I think the language used for the leave campaign really appealed to a disenfranchised group of people. Take back control, our borders etc appealed very much to a group of people who have felt for a long time that they don't have any control. Kicking the elites enhanced that further.
Its a sad state of affairs, because I really can't see things getting better for many of these people.