Just watch the health services. So many doctors already know they can get better pay, conditions, quality of life, etc abroad, and a qualified British doctor can almost take their pick of other countries. We've got a government that's undermining and dismantling the NHS at every opportunity, and the NHS is going to lose the option of quickly and easily hiring doctors from within the EU.
Brain drain is going to be one of the most crippling parts of all this. If the EU is smart they'll make it easy for skilled workers to get out of the UK.
My girlfriend's a doctor and has a ridiculous number of medical friends who've left for Australia in the last couple of years. Pretty sure she's had her head turned after going out there for a wedding last year.