You can’t be a member of the European single market without being a member of the EU.
It’s technically possible for a non-EU member to be in the single market but it requires accepting a lot of rules set by the EU.
"You can't be a member of the single market without effectively still being a member of the European Union."
Theresa May, 18 May 2017
"The single market is dependent on membership of the EU."
Jeremy Corbyn, 23 July 2017
Technically a non-EU member can be in the single market, but that does require following a lot of rules set by the EU.
The European Economic Area Agreement makes Norway, Iceland and Liechtenstein part of the single market but not members of the EU. The EEA countries also take part in various EU programmes and agencies.
They keep out of activities such as the Common Agricultural and Fisheries policies, and can make their own trade agreements.
But this arrangement means accepting rules set by the EU. A major report for the Norwegian government has said that "Norway is in practice bound to adopt EU policies and rules on a broad range of issues without being a member and without voting rights".