The same as it does now.
There is an enormous amount of lies and misunderstanding on this subject.
The EU operates a single market for all its businesses in all 28countries. In order for there to be level playing field for all its citizens/businesses it is agreed that certain laws need to be legislated for.
Legislation has therefore been enacted that takes effect in all 28 countries in order that business can operate fairly and effectively.
There is European wide agreement - dear to my own heart - that there are some issues like environmental that are much more effective if legislated for throughout the EU, like the clean air, clean water etc.
What the EU does not have, and never will have is power over the UKs domestic affairs. So our economic strategy, tax affairs, security, policing, welfare, pensions, criminal law, political life, and on and on is not affected a single jot.
Now this begs the question as to what happens if we come out of the single market.
If our businesses pressure for some sort of return and with 45% of our exports going to Europe, it is inevitable, what are the likely arrangements. My guess is that we will required by law to comply with EU legislation in order to trade. Of course then we will be unable to veto/ block anything we aren't keen on, so I would therefore argue our sovereignty will be totally compromised, with the EU holding all the balls.