[cisstrd]

I don't want to say you are wrong, I just want to clarify further:

Not only was the UK "completely independent 50 years ago", the UK (for the moment let's not care if the UK is a country or a political union) is a completely separate and independent(!)[1] country already and always has been. Parliament can do and undo any(!) law (the principle of "Supremacy of Parliament"), including all the laws that made UK a member of the EU to begin with and all further laws that tangled up the UK closer with the EU. The difficulty is in negotiating a viable exit strategy (because of economic and political consequences), but there is no dispute in the slightest, that the UK is (easily) able and has a full right to simply leave.

The UK always during the last 50 years was sovereign, with every new EU regulation that was "imposed upon them" (they were and are represented in EU parliament, it's not like they had not a say, democracy means compromise) they could choose. Of course having advantages means also accepting decisions of other states in some cases, but they always weighed pro and contra and never ever were obliged to stay. I am not exactly sure how the legal framework in the USA is (I understand it's a heavily federal system), but I doubt it's anyway near the situation of UK sovereignty.

The referendum was not needed, it's not even legally binding. Members of Parliament could have simply made the decision to leave at any given point in time.

[1] It's only not independent in the sense that it of course depends on surrounding countries regarding economic stability, so if one says the UK wasn't independent, then the same is true for any country that has any import/export to other countries and some trade agreements. And in that sense of course UK never was nor will be independent.