There is still a chance the UK won't formally leave the EU, but I think it's slim. Instead, I expect that the UK will officially leave the EU, whilst many of the existing rules and regulations will remain in place. The Norway model was mentioned quite a few times yesterday, but the sticking point here I think is uncontrolled migration, so the final deal will not be identical. In due course, I tend to feel that even the EU will themselves modify the free movement of labour principle, so that won't be specific to the EU-UK relationship. But this development will take time to play out, it cannot be seen to be a direct result of the UK's referendum.
What hasn't been mentioned too much is the Isle of Man's relationship with the EU. Isle of Man is part of the British Isles, not part of the EU, but they adopt many of the EU rules. So the UK solution could end up being influenced by the Isle of Man's arrangement too. Here is an overview of their relationship with the EU:-
Under Protocol 3, the Isle of Man is part of the customs territory of the Union. There is free movement of industrial and agricultural goods in trade between the Island and the Union. EU customs legislation and certain legislation relating to the trade in agricultural goods applies directly to the Island by virtue of Protocol 3.
The Isle of Man neither contributes to, nor receives anything from, the funds of the European Union. Any proposal to amend the text of Protocol 3 would require the unanimous approval of all Member States of the EU. Apart from the requirements of Protocol 3 all other EU legislation is not directly applicable to the Island. The Isle of Man Government may, however, choose to enact legislation that is similar to, or based on, EU legislation if it believes that this is in the Island’s interests. The Island's relationship with the Union allows it to trade with countries in the European Economic Area that are not EU Member States (Iceland, Liechtenstein and Norway) in a fashion generally similar to its trade with the Union itself.
Source:
https://www.gov.im/media/624101/protocol3relationshipwiththeeu.pdf