Dan DiMicco said Britain was "a friend" of America and was leaving the EU for the right reasons.
Both presidential candidates say they are against present plans for a free trade deal between the US and Europe.
Mr DiMicco called for an overhaul of the global free trade system.
"These are not idle threats," he told the BBC.
"Things have gotten so bad that we will leave Nafta [the North American Free Trade Agreement], WTO [the World Trade Organization] and the Korean Free Trade Agreement if we can't get a fair deal."
He added: "The system was gamed for whatever reasons to begin with, the gaming's got to be removed, and it's got to be balanced for the American worker, American business, the American economy and trade deals are going to be walked away from if they can't be renegotiated to the point where they are net-positive for our GDP and they are positive for our good-paying job growth.
"And it is something Donald Trump is not going to walk away from. He is committed to it."
Mr DiMicco said with the present Trans-Atlantic Trade and Investment Partnership (TTIP) proposals "on hold", Britain would be at the front of the queue for any future trade deal once the UK has left the EU.
His comments contrast with those of outgoing President Barack Obama, who - speaking before the UK's EU referendum in June - said Britain would go to the "back of the queue" for trade deals with the US if it left the EU.
When asked if the US would do a deal with Britain ahead of the EU, Mr DiMicco told me: "Absolutely.
"First off they are our friends, they have always supported us, and we've worked together, and they are leaving the EU in our estimation for the right reasons.
"They have lost control of their economy, the job creation engine, so why shouldn't we be working with like-minded people before we do a deal with anybody else?"
Britain will be offered a free trade deal before the rest of the European Union if the Republicans win the US presidential election, Donald Trump's trade adviser has said.