The EU Single Market exists entirely for the benefit of the European Union Commission.
The EU Single Market is the mechanism by which the EU Commission restricts suppliers access to European consumers and restricts European consumers access to suppliers. The EU Commission sells access to suppliers, the Commission skim money in a variety of ways. But primarily it lets producers charge artificially high prices (which EU consumers have no choice but to pay) and takes a cut of this money raised through exploitation of the European people.
Outside the EU Single Market, UK consumers will have a global choice for suppliers - if the EU does have the cheapest suppliers, then UK consumers may chose to continue to use their current suppliers.
If, however, as is likely, produce can be sourced elsewhere more cheaply then the UK consumer can choose to purchase elsewhere. This will result in savings to the UK consumer, an increase in UK trade with 'the rest of the world' and a drop in UK trade with the uncompetitive, price rigged EU.
As a trade body and government the EU has produced a mish-mash of law and trading regulations/standards - this is something that should never have been allowed. Product standards (apart from the most basic safety) is no business of the law makers. A consumer is well capable of deciding what standard/specification of item they require and communicating this to a supplier. And as this specification will form the contract, the only law required is that required to generically enforce contracts, the specifics of the contract are irrelevant.
Whole swathes of EU Law are entirely unnecessary, and worse are damaging to innovation, development and progress - leaving the EU should remove these laws from applying in the UK.
However, Theresa May has already stated that all EU law will be adopted into UK law(!) Even specifically confirming that laws on (bent) bananas, sausages etc will be included. Theresa May has suggested that once transferred each law can be reviewed and a decision made on whether to retain it, repeal it or enhance it. But as we have two years before the EU treaties cease to apply, it seems odd that this work cannot be started now and completed by the time the Article 50 notice period expires. If it cannot be done in two years when it is the governments main focus, How can anyone imagine it will ever be done? It is worth remembering that even the broken, bogus 'Barnett Formula' was a one off temporary fix in the late 1970's that has been in desperate need of revision but now after almost half a century has not be changed, also refom of the house of lords - which has been in progress even longer to no good effect.
In truth the UK parliament has always been soverign - even with the 1972 EU Legal Supremacy act it was only bound to its own choice - it could have repealed it anytime.
The referendum result is not actually about the EU at all - it is about the UK parliament not acting in accordance with the wishes of the British people - for decades our parliament kept us as unwilling victims of the Brussels bureaucracy, and resisted our calls to be heard (by referendum) - now we have spoken and must ensure parliament never again think they can ignore our wishes.