Hard economics
The EU sells more to the UK than the UK sells to the EU so any restrictive practice would hurt the EU far harder than the UK so it is in no ones interest to cut free trade.
The cross broader movement of skilled labour is also an economic benifit to all so I see very little change in that area, in some EU states it is next to imposable to get a pilot job if you are not a local so no change in France & Spain other EU nationals will still face discrimination.
What will change is the work shy who want to live from the UK social security system won't be able to do so that the European court won't be able to override the UK system using the so called Human rights laws. People like the ring leader of that vile gang in the north of England who abused young girls can be extradited after the long prison sentence he is serving rather than the European court allowing him to stay here because of his so called human rights.
The European court has perverted the course of justice to favour the criminals when it is the human rights of the victims of crime that should be paramount.
Returning to aviation the FTL can return to being based on scientific research rather than the latest rubbish from EASA that can only be based on the wishes of the likes of MoL.
Consideration should also be given to moving UK aviation to align it with the FAR's much better to have an industry based on a practical & pragmatic set of rules that have a good safety record that have the very good UK flight safety system watered down when EASA panders to the nations of Southern Europe who's safety records don't stand up to much scrutiny but are over heavy on paperwork ( back to the new FTL ).
I can see the brexit prompting the nations of Northern Europe who pay their taxes and work hard rethinking their relationship with the EU and leaving the nations who's leaders spent money they did not have to buy votes to fend for them selfs paid for by the Germans who for historic reasons can't drop the EU project ........ Let's hope the German's can get the new immigrants to work hard and build enough BMW cars to dig themselfs out of Merkel's mess.