The UK is currently a Contracting Party to the European Economic Area (EEA) Agreement, and exit from the EU does not necessarily imply exit from the Single Market (i.e. withdrawal from the Agreement). Exit from the EEA would require that extra steps be taken, either unilaterally by the UK or by the other Contracting Parties to the Agreement.
There is no explicit provision in the Agreement for the UK to cease to be a Contracting Party other than by unilateral, voluntary withdrawal, which requires simply the giving of twelve months’ notice in writing (Article 127). A commonly held assumption that only EU and EFTA members can be Parties to the EEA Agreement – and hence that the UK has to be a member of one or other of these two organisations to be in the Single Market – is not well grounded, although UK consideration of an application for EFTA membership is an option well worth exploring in its own right.