The question below is about the EU’s Single Market.
As a member of the EU the UK is also a member of the EU’s Single Market. All members of the Single Market have to accept the supremacy of EU courts, accept free-movement of people which means no control over immigration from other EU countries, and they have to make payments to the EU budget.
If the UK were not a member of the Single Market we could still sell goods to EU countries just as the USA, Canada, Japan and all the other countries outside the EU do. We could therefore still access the Single Market even if we were not a member although it is likely we would have to pay a tariff on each transaction just as we do when we trade with other countries outside the EU like the USA.
The question below is about the EU’s Customs Union.
The EU’s Customs Union means that all EU members have a common customs border with the rest of the world and no customs border with one another. Customs borders exist so that countries can charge taxes or tariffs on goods they import. Free trade agreements are agreements between countries to reduce or remove tariffs on goods they sell to each other.
As a member of the EU Customs Union we can buy and sell goods and services from other members of the EU Customs Union without any import taxes or tariffs. However the EU Commission negotiates tariffs and trade deals on behalf its Customs Union. As a member of the EU Customs Union we are therefore NOT able to negotiate tariff reductions in free trade deals with other countries and have to accept whatever the EU decides to negotiate.