Yes, in a way, see NAFTA. Trade and travel agreement. Although the EU/Swiss deal is more open border-wise.
I do agree that the motivation for change is the same between the UK and the US. Unaccountable leaders (elected and regulatory both) working against the people, results in the people throwing out the leaders and eventually the government. Our leaders want a country in name only.
That is a very accurate and succinct way of describing it.