You can negotiate plenty of labor movement just with some simple qualifications, like not having a criminal history, being an eu citizen for 5+ years, no access to welfare for 3 years, things like that. I think most brexit supporters would go for that. The opposition is not to immigration in general from what I understand, but to uncontrolled immigration with which the UK parliament has no control.

Modern visa granting can be done electronically like the U.S. ESTA and could easily be achieved with little disruption. It could also prove a handy earner for a small fee.

I think it is misrepresenting the majority of brexit supporters to say they don't want any immigration. All the ones I talked to just wanted to have a say, and the EU did not give them that.