Depends on the legal framework that is negotiated for the future relationship, how extensive it is, how much we sign up for etc. The less we commit the less we get. Some aspects are already off the table. The UK police will not have access to the EU data base and the European Arrest Warrant will not apply. Audio Visual services will not be included in any future deal which has lead to a reduction in companies here with channels aimed at EU market.
In short it is down to us and whether we sign up for a myriad of EU schemes and programs or not. The more we sign up for the less things will change.