The Norwegian situation is an interesting one. They rejected full membership of the EU in 1994.
Does Norway have free trade with EU?
As member of the European Free Trade Association ( EFTA ), Norway seeks to conclude bilateral Free Trade Agreement in the so-called EFTA framework. This means that Switzerland, Norway, Iceland and Liechtenstein can negotiate a Free Trade Agreement with a respective third country via EFTA .

Thus they avoided The Maastricht Treaty, known formally as the Treaty on European Union, the international agreement responsible for the creation of the European Union. They pay €0.40billion annually for the privilege.While not formally a single market membership fee, this money is linked to trade relations with the EU. Norway's EU minister said last year that “We gain from being a member of the single market. Norway is also in the Schengen area whereas the UK has never been a part of it. Norway is not part of the customs union. So it sets its own tariffs on goods imported from outside the single market. But Norwegian goods (with exceptions for farm produce and fish) are imported tariff-free into the EU.
    Personally I would be happy to see some brexit result approximating the Norway model. But I doubt the EU would agree, too many in Brussels and Strasbourg would be trampled in the rush to follow us.