Of course they did - but they still traded with Europe and existed in the international community. They still had rules to play by that had to be worked out very carefully; when they didn't, we got the Opium Wars, or even the Declaration of Independence can be considered a consequence of thinking a country can just do what it wants when it wants.
And if Britain doesn't want to play by EU rules, the question becomes what rules *do* they play by. And as I say, the choices are things like WTO rules, Switzerland-plus rules, or Euro-sphere rules where Britain gets treated like they're in close proximity to the EU as though they're Israel or Turkey. And none of those options throw out immigrants. None of those options bring trade dispute arbitrations to exclusive UK jurisdictions. Most of those options require putting up a comprehensive border with Ireland where right now it's very casual - and that's a lot of money and risks a renewed conflict with Ireland. And none of them guarantee to British corporations that they'll get a better deal after Brexit than before Brexit.
What Boris Johnson was promising was unachievable. What pro-Brexit voters were asking for was unachievable. And lo and behold, two Prime Ministers have yet to achieve it. Go figure.
And it is a massively technical subject - we couldn't POSSIBLY describe it properly in comment boxes like this - but that's exactly why putting a technical decision to a public vote with poor information (on both sides!) was a mistake.