No one can predict with any degree of certainty what the labour market consequences of the UK leaving the European Union would be. There are so many policy options, institutional factors and their interactions that determine labour market performance, which may play out in different ways (visa quotas, residency requirements, corporate behaviour, trade agreements, reaction in other countries, to name but a few), that to try to anticipate every possible scenario would be heroic in the extreme.
So can anything be said? Perhaps one way is to set out the facts as we know them with regard to the position of EU-nationals living and working in the UK and the effects so far, if any, on the labour market prospects of UK nationals. Knowing what happened when EU migration to the UK increased might give a hint as to what could happen if EU immigration turned into forced emigration.