Here's a list of the countries that have free trade agreements with the U.S.:

https://ustr.gov/trade-agreements/free-trade-agreements

The UK is included in the proposed Transatlantic Trade and Investment Partnership (T-TIP) as long as the UK remains part of the European Union.
Free trade agreements are a relatively new phenomenon. Most of them appear to have been concluded during the regime of George W. Bush. See this list (click)

Free trade agreements have been the source of many conservative conspiracy theories in the U.S. Many people think that if we negotiate a trade agreement with another country, we somehow cede our sovereignty to them. Bill Clinton and Barack Obama met with a lot of opposition to their efforts to join free trade agreements because the Republicans didn't trust either Clinton or Obama. Bush met no such opposition.

Note that these are free trade agreements. Other trade agreements go back centuries, and I'm sure the U.K. has made many, more limited trade agreements with the U.S. in the past.

Here (click) is an article from The Guardian about Obama's "back of the queue" speech. No doubt, some fussy person would have been offended if he'd used the more American expression, "back of the line." And I'm sure that many American conservatives were offended by Obama's attempt to honor the UK by using a British expression. Sometimes, you just can't win.

No doubt, the next U.S. President will not be as wise or intelligent as Barack Obama. Listen to what the man says, and don't get fussy about the "queue." There is strong disagreement among American conservatives to free trade agreements, and negotiating such agreements is close to political suicide for Democrats. So, yeah, if the UK withdraws from the EU, it also withdraws from the Transatlantic Trade and Investment Partnership. And it will take twenty years to negotiate a separate US-UK agreement. Those are the facts. Consider them when you face the vote to withdraw from the EU.

This American thinks it would be a mistake for the UK to withdraw.

-Joe-