The UK was completely independent 50 years ago -- that is, some people still working got their first job out of school when that was still the case. And it's not like it integrated with Europe overnight - or going to leave it overnight.
European's complete freedom of movement as we know it today is about 20 years old, not 50. I still had to go through border checkpoints in Europe less than 30 years ago. It was more of a formality even then, but the checkpoints were still there and operated. Half of today's Germany (the east) was, for most economical purposes, nonexistent at the time.
Only about 50% of the UK's export and import is with the rest of Europe. How much of NC's export/import balances are with the rest of the US?
(Bonus: Texas was, in fact, independent for a short while two centuries ago -- but otherwise you'll find NC is as (in)dependent as Texas on the rest of the US, in the ways that UK is not dependent on the EU.