The UK will remain a member of the EU for AT LEAST the next 2 years, and 2 years is measured from the moment the UK formally notifies the EU it intends to leave . The U.K. is in no rush to make such a notification . When the process does eventually begin, it is highly probably that an agreement to maintain the status quo with regards to labour will be reached.
Much more relevant is a discussion of the effects of the referendum on demand for air travel to and from the UK....
BA have already highlighted the fact that business travel demand was down even before the result of the referendum. This is more relevant and of immediate concern, than what may/may not happen in 2 years from now..