Sir Andrew Cahn backed the US president, undermining attempts by a furious Downing Street to fight back against the bombshell dropped in Washington.
Sir Michael Fallon, the former defence secretary – who will vote against a deal he branded “doomed” – also warned that “brushing off” Mr Trump’s embarrassing comments would not work.
No 10 was thrown on the back foot when the president described the Brexit proposals as “a great deal for the EU” and “a very big negative” for the UK’s aim of striking its own trade deals.
Sir Andrew Cahn, the former chief executive of UK Trade & Investment (UKTI), agreed, telling BBC Radio 4 that, unusually, the president “is actually speaking the truth”.
Pointing out any trade talks would not be able to cover key US interests such as “sending their chicken to us, their cars”, he added: “In the end there just wouldn’t be a deal.”
Sir Andrew said the Brexit plan was likely to leave the UK “stuck within the EU customs union for the foreseeable future” – restricting bilateral trade deals to services only.
“The deal Mrs May has come up with doesn’t tell us what the long-term trading arrangements between Britain and the EU would be,” he said.
“So, after the transition period is finished in two or three or four years, anything could happen.”
Sir Andrew, who advised on setting up the single market in the 1980s, added: “It will be very difficult to do independent trade deals for as long as we can see looking forward.”
The warning came as Sir Michael, who resigned a year ago, called for Brexit to be postponed “for two or three months”, to allow negotiators to go “back to Brussels” for a better deal.
“It’s no use us just brushing that off, saying ‘no, no we can do a deal with America’,” he said.
“He’s the president of the United States, and if he says it’s going to be difficult, then it certainly looks like it’s going to be difficult. This is not a good deal and we need a better deal.”
At the White House on Monday, Mr Trump said: “Sounds like a great deal for the EU. I think we have to take a look at seriously whether or not the UK is allowed to trade” – a reference to signing trade deals.
“Right now, as the deal stands, they may not be able to trade with the US and I don’t think they want that at all. That would be a very big negative for the deal.”
Later, the prime minister, speaking on a visit to Wales, insisted the “political declaration“ agree with the EU would allow the UK to strike its own trade deals.
“It clearly identifies that we will have an independent trade policy and we will be able to do trade deals, to negotiate trade deals, with countries around the rest of the world,” she said.
“And, as regards the United States, we’ve already been talking to them about the sort of agreement we could have with them in the future.
“We’ve got a working group set up which is working very well, has met several times, [and we’re] continuing to work with the US on this.”
And David Lidington, Ms May’s de facto deputy, shrugged off Mr Trump’s comments, saying: “I don’t think it was that unexpected.”
He added: “I think it was always going to be challenging to do a deal with the United States. The United States is a tough negotiator, President Trump’s always said very plainly ‘I put America first’.”
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