Staying in the single market would reduce the UK to an associated country, which has basically all the same duties and all the same to pay, but no say whatsoever in the decisions the EU makes and gets no support. There are literally no benefits of downgrading a membership to an associated status.
As you've no doubt noticed, there is a certain lack of political and economic awareness on the part of many of the Brexiters. The benefits of downgrading are that we'd still keep the EU and the economic advantages it brings, yet they'd still be able to tell the brexiters we've left, and giving a knowing wink at the remainers.
Seriously. This is likely.
Another possibility of staying in the single market is that the UK negotiates its own free trade agreement with the EU. The downsides of this are that it would take extremely long while the economy suffers and that the rule "The bigger partner determines the conditions" still applies. To get such an agreement the UK would have to swallow everything the EU wants. That's simply because the UK depends far more on the imports from the EU than the EU on the imports from the UK.
I don't think that's an option. Everything the UK does at the moment can also be done in the EU, and that's really bad for us. Any one of the nation states can veto any agreement made on account of their own interests (such is their "lack of sovereignty"

).
Not only that, but the various Parliaments around the UK have demanded a power of veto over any deal done, as well as others demanding a referendum on accepting any deal.
So in other words, we leave, spend 3 years negotiating a deal, then the Daily Mail doesn't like it and convinces the public to vote it down again... then what?
And the EU is in a far stronger position to negotiate. Without Germany and France being benevolent towards the UK it's certain that the deal is not beneficial for the UK in any way.
France is actually pretty hostile to the UK right now, and it isn't just because we stirred up a hornets nest with the National Front. Let me break this one down.
http://www.theguardian.com/politics...g-briefing-free-trade-free-movement-france-uk
Hollande is not only saying "Start article 50 now!" he is also telling us, in no uncertain terms, that he will not let us remain in the free market without free movement of people - and he is well aware of the focus on that in the UK.
He is basically daring us to jump. But why?
1. We aren't the only nation with a neo-fascist party like UKIP gaining traction. Hollande has La Pen and the far-right to worry about.
2. We leave, and France courts the big financial institutions in London, which gives their economy quite a serious boost that, up until now, the UK has enjoyed. Hollande will benefit greatly from that.
3. The UK falters, the economy shrinks, unemployment rises and a recession takes hold - a powerful lesson for the French people and a weakening the position of Hollande's domestic enemies.
and of course
4. Islamic immigration is a huge hotbutton issue in France right now. But if the UK leaves the EU. The French border authorities suddenly have a very easy way to limit the immigration of Muslims into France. Rather than stopping them at the ports and detaining them, as they currently do, if they find Muslim refugees/illegals on cargo ships bound for England the French may well simply leave them there to travel across the border. It's also possible they might actually "encourage" Muslims stowing away on such ships to move onto UK bound vessels. In addition, the Asylum "jungle" in Calais will have to be moved to UK soil, which will further give Hollande a boost domestically.