A The government insists that free movement of people will end after Brexit, but the White Paper states that the United Kingdom "will want to continue to attract the brightest and best, from the European Union and elsewhere".
Ms May's "business-friendly" Brexit plan - which would keep Britain in a free trade zone for goods with the European Union but mean it has to share some European Union rules - was agreed by her cabinet only last Friday after two years of wrangling since Britons voted to leave the bloc in a 2016 referendum.
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".
May's critics have said, however, that she reins in criticism of Trump because of the strong desire of many in her Conservative Party to reach a trade deal with the United States after Brexit.
Debate in the U.K. Parliament's lower house was formally suspended for five minutes Thursday, when the announcement of a key policy paper on the nation's planned exit from the European Union descended into chaos after members of parliament complained they hadn't received copies of the document.
Trump had already cast doubt on May's Brexit plans earlier in the day after a North Atlantic Treaty Organisation summit in Brussels, where he provoked a crisis session to force allies to raise their defence spending.
When asked about the ongoing negotiations between May's government and the European Union over the terms of their divorce, Trump told The Sun: "I would have done it much differently".
Trump told the Rupert Murdoch-owned newspaper he had advised May on how to conduct Brexit negotiations, "but she didn't listen to me".
He added: "I would have done it much differently".
"This is incendiary even by his standards", Adrian Morrow, a British reporter with the Globe and Mail, said of Trump's comments.
Foreign Minister Boris Johnson also resigned citing his disappointment with the proposals, which he said "stick in the throat". I think she is a nice person. I never said anything bad about her. "I'm just saying, I think he'd be a great prime minister".
More than 60,000 people have signed up to demonstrate in London on Friday when protesters intend to fly a large balloon over parliament portraying Trump as an orange, snarling baby.
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London". I haven't been there in a long time. "I just want the people to be happy".
Mr Trump has come to blows with the London mayor before, with Mr Khan the subject of many a tweet from the president.
"Take a look at the terrorism that is taking place".
Khan earlier urged Londoners to keep Friday's main protest "peaceful and good-spirited", saying the message went broader than Trump.
Prime Minister Theresa May's government is trying to satisfy Britons who voted for their country to leave the bloc, but to set an independent course without hobbling businesses, security agencies and other sectors that are closely entwined with the EU.
You have a mayor who has done a bad job in London.
Director and chief executive Liz Cameron said: "We welcome the detail provided on the UK Government's approach to mobility, including the statement of intent to operate a UK-EU Youth Mobility Scheme and visa-free travel for tourism and short-term business activity". "I think you are losing your culture".