"If they do that, I would say that would probably end a major trade relationship with the United States", Mr. Trump added.
But many Brexit supporters have cast May's negotiation as a betrayal, including lawmakers in her own deeply divided party, who have warned May might face a leadership challenge. "But it is too bad what is going on".
But the plan has infuriated fervent Brexit supporters in May's Conservative Party, who think it would limit Britain's ability to strike new trade deals around the world.
It comes just days after Mr Trump declined to say whether Mrs May should remain in post, said he had "always liked" Boris Johnson, who quit as foreign secretary over the Chequers agreement, and described the United Kingdom as being in "turmoil".
Trump accused the British political leader of "killing" chances of a U.S. trade deal by ignoring his advice on Brexit and taking her own, "softer" approach.
He is due to meet the Queen at Windsor Castle following his talks with May, before flying to Scotland for a two-day private visit and break before jetting back to the US.
He said "the deal she is striking is a much different deal than the one the people voted on".
"The Americans can't believe, quite frankly, what a mess we're making of Brexit", he told the BBC. It was agreed by her Cabinet only last Friday after two years of wrangling since Britons voted to leave the bloc in the referendum.
While accepting that financial services will take a hit after Brexit and not enjoy the same levels of market access as now, the White Paper points out that Britain will reserve the right to diverge from European Union financial regulation after Brexit while still observing global worldwide standards. "That is exactly what we will do".
Speaking about the prime minister's strategy, President Trump said, "I would have done it much differently".
"I think he has done a bad job on crime, if you look, all of the terrible things going on there, with all of the crime that is being brought in", Trump said of Khan.
Mrs May appealed to European negotiators to "engage" with her blueprint in the same spirit of respect that she said her government was taking toward the EU's own principles and red lines. The plans laid out in a 98-page government paper give Britain's most detailed answer yet to the question of what will replace it.
In a podcast for the Brexit Central website, he added that if changes were not made to the plans, Tories would be "screwed" in the next general election.
Even United States President Donald Trump took a view. While there would be "no tariffs on any goods", the U.K.'s vast services sector will suffer significant disruption.
The UK Government has published its long-anticipated Brexit white paper earlier today, proposing the establishment of a free trade area for goods between the UK and the European Union.
Under the blueprint, Britain would stick to a "common rulebook" with the European Union for goods and agricultural products in return for free trade, without tariffs or border customs checks.
Mrs May will host Mr Trump and his wife Melania at a lavish dinner at Blenheim Palace this evening. In which, the Prime Minister hopes will avoid a hard Brexit and a hard border with Northern Ireland and the EU.
Free trade would not apply to services, which account for 80 percent of the British economy.
"I think allowing millions and millions of people to come into Europe is very, very sad", he said.
The UK is seeking three agreements, on economic partnership, security and defence, and cross-cutting co-operation - monitored by a "governing body" to set the political direction of EU-UK relations and a joint committee to provide technical expertise.