The FT explains how complicated this is:
Membership of the EU’s customs union — that is, having a common external tariff applied to imports from the rest of the world — is a separate issue to membership of its single market. Norway, for example, is a member of the single market but not of the customs union, enabling it to protect some of its producers with higher tariffs than allowed in the EU. If it wants, Norway can also sign trade deals with third-country governments permitting imports at lower tariffs.
However, in order to prevent countries such as Norway becoming a backdoor into the EU market, Oslo is obliged to apply complex “rules of origin” to its exports, ensuring that they have substantially been made in Norway rather than imported from, say, China and re-exported to the EU. This, plus the need to comply with customs paperwork from which EU countries are exempt, imposes considerable costs on Norwegian companies selling goods to the bloc.
For Norway, whose exports are dominated by primary products like crude oil, this may not pose too great a hardship. For the UK, whose goods exports are generally more complex and involve the use of imported inputs, they could prove a serious handicap. On the other hand, if the UK stays inside the EU customs union and is forced to apply the same tariffs as the EU, that will in effect preclude it signing any meaningful trade deals involving goods trade with any other economy.
The big question the UK needs to figure out is the following: Is it more interested in maintaining its current liberalized trade relationship with the EU, or exploring options for liberalizing trade with the rest of the world?
