So, you're right. There is an excellent Wikipedia article [1] that goes through the research done around this.
That said, the Prime Minister has said consistently since coming to power and discussing Brexit negotiations that immigration - and specifically free movement - is a key criteria to their stance. They wish to end it, as much as possible.
During the campaign, Farage's alternative Leave campaign made this the central issue for many of the numerous debates that were had, including a rather sickening photo on the back of a lorry.
When you go into many communities and discuss Brexit - as I did both before and after the vote - the main driver was immigration, specifically in the context of Calais and middle eastern refugees. It doesn't matter that this has nothing to do with EU membership, it was perceived all through the Summer as EU members losing control and us being "at risk".
In the days after the result, there was a recorded rise in hate crime, my local Polish centre being attacked, people being shouted at in the streets. I even had one colleague who is Scottish but has a more olive tone to his skin than most Brits being told to "fuck off home" the day after the vote by a passing van driver.
The fact that immigration was being used like this was a major part of the debate for me. I work with many EU nationals, many of whom were concerned about how the debate was structured, and shortly after felt threatened.
So, we - those who campaigned for Remain - predicted that immigration was going to be the central issue, it became the central issue, attempts to diffuse it by correcting blatant lies about the effects of immigration were not picked up by many, arguments to enflame people did get traction, and after the vote immigration has become a central tension point in both our society and our negotiating position.
It's fair to say, immigration was a major - if not the essential - factor in most people's minds when voting.
What's interesting is how that breaks down. Lord Ashcroft's polling puts immigration further down the list, but then he was sampling people in more affluent cities that were broadly Remain, because more people live there. In fact when you get out into the sticks, it's way higher, especially in lower income homes.
You voted the way you did for the reasons you did. However the main driver of at least one Leave campaign - and to some extent both - was immigration, and all the discussions are now framed in that context for that reason.
[1] https://en.wikipedia.org/wiki/Causes_of_the_vote_in_favour_o...