It is sometimes claimed that Britain is ruled by Brussels. This is not accurate: the British Government and Parliament are far from powerless. Britain controls its own budget, currency, health service, armed forces, criminal law etc etc.
Decisions taken by the EU are made in, not by, Brussels: they always involve British Government Ministers and MEPs elected by the British people. If Britain wants access to the EU single market it will have to follow many EU rules, whether it is an EU member or not.
Britain would still have to abide by the rules of international bodies like UN, NATO, World Trade Organisation and IMF unless it quit them too.