There are some breakdowns of who voted what way, but they're not as strong as people on the internet would have you believe. But:

The old tended to vote for Brexit more than the young.

The uneducated tended to vote for Brexit more than the educated.

People in areas that had experienced recent immigration tended to vote for Brexit more than those in areas that had high historic levels of immigration.

There are some complexities and corner cases to go with that (for example, people whose ancestry can be traced to the Indian sub-continent often voted for Brexit because they felt European immigration was being unfairly prioritized over RoW immigration).

Bundling all that up, I'd say the main driver behind Leave was immigration (they didn't like it), and the main driver behind Remain was having a stake in society as it currently exists (if you think you're doing ok, you're not going to vote to overturn the applecart).

This is just my opinion, of course. But nobody, on either side, will ever admit to those reasons. It's all just horribly entrenched, and they've had years to dig in and convince themselves of new justifications.