EU rules on non-discrimination and mutual recognition, as well as supra-national EU regulations, allow most UK producers of goods and services to sell directly to EU customers without having to navigate through additional domestic government regulations. The rules are broad and have a strong enforcement mechanism. Generally speaking, if UK companies comply with domestic regulations, they may sell in the rest of the EU (as noted, with a few exceptions).
That's the whole point of the single market, a level playing field across all members with the same rules. Now you may tell me about increased sovereignty, controls on immigration or whatever other fantasy you are reading in the daily express at present, but to suggest there will not be a fundamental cost in our trading relationship with our biggest market after Brexit is just la la land.