I think a lot of people who argued for brexit did so mostly out of ignorance.
"There are regulations on bananas, this makes things inefficient!" (forgetting that the regulations on bananas was about categorising them, not forbidding sale).
They felt out of touch and disconnected from EU parliament, and it seemed complicated and scary. Ironically the reason it's so complicated is because it's a lot more democratic than our own systems- but instead of attempting to understand it they threw their hands up and thought "since I didn't vote for every person who works there, it must be undemocratic!"
It's very true that there was an anti-migration sentiment inside brexit, but I wouldn't go nearly so far as to say that this was the only feeling people had.
I'd say it's mostly feeling a loss of control, which they couldn't place and our politicians were not open enough about explaining that this loss of control of the population was caused by.... the politicians themselves.