Every non-EU country that can visit Schenghen area without a visa, allow Schenghen people to allow that country without a visa in return.We might need a Schengen Visa to visit the EU though... probably won't happen, but it is possible.
No idea how this will work for UK, but it will be an irony if UK is forced to have free borders (for short term visits) from Schenghen area in order to safe its tourist industry.