Oddly enough, bilateral traffic rights existed quite satisfactorily in the days before the EU, right up to the level of fifth-freedom.
In the early 1960s Aer Lingus had more fifth-freedoms that any other European carrier, and that from a nation with a population of fewer than three million at the time and little in the way of an economy. Yet they negotiated like pros and got what they wanted.
The UK will remain an attractive destination for European carriers and they will pressure their Governments to pressue the organs of the EU to negotiate bilaterals.