The US Ambassador to the UK says negotiating a trade deal post-Brexit would be "much more difficult" if the UK is in a customs union with the EU.
Woody Johnson also said it would be "more challenging" for the UK "to get control of [its] own trade policy".
But he said President Donald Trump is still hopeful doing a "robust, big, very generous trade deal" with the UK after Brexit.
President Trump will come to the UK for a state visit in June.
He and First Lady Melania Trump will be guests of the Queen at Buckingham Palace, and attend a ceremony in Portsmouth to mark 75 years since the D-Day landings.
He will also have official talks with Prime Minister Theresa May at Downing Street.
A number of campaign groups have already said they will hold protests during the trip - set for 3 to 5 June.
Shadow foreign secretary Emily Thornberry has also criticised the visit, claiming it will be "a giant waste of taxpayers' money" as the US will never agree a trade deal with the UK unless a solution is found for the Irish border after Brexit.
But Mrs May said it was an "opportunity to strengthen our already close relationship in areas such as trade, investment, security and defence, and to discuss how we can build on these ties in the years ahead".
Last time President Trump came to the UK on a "working visit" in July 2018, tens of thousands of protesters took to the streets in central London.
He managed to avoid the crowds by meeting the Queen at Windsor Castle and Mrs May at Chequers, and travelling by helicopter.
But Mr Johnson said President Trump was looking forward to returning and was "never apprehensive about anything".
The Ambassador said the president would not be kept out of view as he liked to be "out with the people", and talks between the two countries would continue "despite protests or anything else".
He added: "The British know this is a very, very critical relationship to the future of Britain, and so welcoming the president here is a really good symbol for the future prosperity and security of this country."