The single market is not some sort of solid entity with a membership independent of the EU. It's a casual term for a zone of common regulation, standards and trade.
No country outside of the EU fully implements the "four freedoms" in the same way the EU member-states do. I don't see why we should, or how that would fairly represent the result of the referendum.
As a more general point, people seem to constantly want to pick an off-the-shelf solution to our future relationship with the EU. That's frankly silly - countries outside of the EU have adapted their relations to suit their particular needs. Even the EEA countries share many common economic characteristics and those are reflected in the EEA agreement. Britain needs to do the same, not just to expect there is a default we can fall back on. Annoying and difficult, but that's the nature of disentangling ourselves from such a complex economic bloc.