Is it already certain that all benefits of Schengen remain? (likely) Visa-less work in the rest of EU? Visa-less study? Are travel costs going to remain the same? Will the UK have to renegotiate tourist visits with countries which had deals with EU, rather than separate countries? These are factors that could change as far as I know.
i would be surprised if we didnt get visa-less travel to shengen and visa-versa. visa requirements for study are generally pretty easy (can you afford it) and for work are a good thing. most eu countries already require some form of work permit (for tax purposes), they are easy to obtain and amount to the same thing as a visa. travel costs are based on market forces and government policy, we could make travel even cheaper if we left by reducing taxes if we chose to. the costs of operation are otherwise the same
But why would they choose to make things easy for us if we are essentially giving them the middle finger? We can't pick and choose what we fancy from the EU while simultaneously walking away..
I'd be surprised too. But right now it's an unknown, right? Also, there are multiple EU-related programs for scholarships which could go away for the UK people. Work... we'll see.