Access to all markets across the world should be the right of every nation. Membership of a group of countries which ties in to one set of markets simply puts a stranglehold on all the nations in that group. If the U.K. is to be denied access to the single market, which presumably means that the other E.U. members won't be allowed to trade with the U.K. either, that will effectively force the U.K. to find their trade partners elsewhere and will inhibit a rich source of commercial interaction for all concerned.
I believe that countries should not have to enter into anti-democratic, bureaucratic regimes to be able to trade easily with one another. Global trade is crucial to healthy and innovative economies and Europe would only be hurting itself out of pride to not allow the UK access to their market.
The UK economy could thrive outside the European Union, but may not form part of the single market. after Brexit the UK would be part of a European "free trade zone", one that already exists from "Iceland to the Russian border" but not part of the single market as they are at the moment.
No, the U.K. should not be able to access the single market after it leaves the EU. Allowing it to continue trading with the member countries without the imposition of tariffs could provide incentives for other member countries to also exit the EU. This could lead to the entire system to collapse.
Following the UK's referendum and the pending activation of article 50, I do not believe that the United Kingdom should be able to get all of the benefits of the single market without accepting free movement of peoples and labour from all other European countries. I do not believe that they should be a special case.