Just to add to @denis-de-bernardy's answer, one of the main reasons given during the campaign for leaving the EU was the ability to conduct trade deals with non-EU countries which being in the EU didn't allow the UK to do. If the UK could sign a trade deal with Germany once the UK has left the EU, then it would stand to reason that Australia (to give an example) could sign a trade deal with the UK without the UK leaving the EU.
Being a member of the single market is different and doesn't prevent a country signing trade deals with third countries (for example, Iceland and China recently signed a trade deal).