We are not governed by the EU, we are the EU, as are France Germany, the Netherlands, Belgium, Poland, Italy, Greece, etc etc etc. We all appoint one commissioner each and we agree on the rules and regulations. Of course we do not get our way all the time. Why should we?
Most EU legislation is legislation that would have gone through our Parliement anyway, which is why the British Parliament has already passed an Act subsuming the majority of the EU legislation into British law.
If we wish to continue exporting to the EU we will have to make sure all our exports accord with the standards that the EU set. All that will happen is that in the future we will no longer have a say in what those standards are.