Fox will meet Trump's trade representative, Robert Lighthizer, in Washington to kick off two-day talks this week, which DIT said would "explore ways to strengthen our trade and commercial ties ahead of exit, consistent with our European Union membership obligations".
However, under current European Union rules, however, Britain remains a full member of the bloc and, as such, is unable to negotiate trade deals outside of Brussels.
Fox said: "The US is our single largest trading partner".
"Liam Fox and Boris Johnson must not be able to stitch up trade deals overseas and impose them on the country", he said.
The row is an early sticking point in the Brexit negotiations, and the European Parliament has warned that trade talks can not kick off until more progress on citizens rights is made.
Speaking on the BBC, Fox, who campaigned for Brexit, said that while the United Kingdom will be "out" of the EU's single market and customs union, it may still "decide to implement some of the practices of those for a period of stability, which we believe is in the interest of United Kingdom business and our overseas investors".
The BPC urged the government to back British farming and its world-leading food safety standards.
"The EU itself estimates that 90 percent of global growth in the next decade will come from outside Europe", he said, "and I believe as the head of an worldwide economic department that this is an exciting opportunity for the U.K.to work even more closely with our largest single trading partner, the U.S". The British Poultry Council slammed the notion of importing chlorine-washed chickens as part of a "makeweight in trade negotiations with the U.S". "We won't accept a race to the bottom on standards".
It is thought that in striking a trade deal with the United States post-Brexit, accepting chlorine-washed chicken would smooth the way.
The Trump administration has launched a review of the steel industry and is weighing tariffs on imports that could spark retaliatory action.
"We want to do this quickly as a moral imperative because we want to take away the anxiety of all of those four million people and give them some certainty in their future", he told a news conference after talks with the Czech foreign minister Lubomir Zaoralek in Prague.
Theresa May's spokesman has said that maintaining safety and public confidence in food was of the highest priority, but that it was too early to get into the specifics and "hypotheticals" of any deal.
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