It follows the Republican frontrunner's call for a "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on".
Mr Trump's comments were designed to capitalise on a shooting by a radicalised couple in San Bernardino, California, that killed 14 people.
But they have drawn condemnation both at home and abroad.
In the UK, some people have signed a petition calling on MPs to impose a bar on Mr Trump, with the number of signatures hitting 120,000 just before 1pm.
"The UK has banned entry to many individuals for hate speech," the petition reads. "The same principles should apply to everyone who wishes to enter the
"If the United Kingdom is to continue applying the 'unacceptable behaviour' criteria to those who wish to enter its borders, it must be fairly applied to the rich as well as poor, and the weak as well as powerful."
A petition needs to reach 100,000 signatures to be considered for debate in the Commons.
Across the Atlantic, the White House launched a rare attack on a presidential candidate as spokesman Josh Earnest called the proposal unconstitutional.
"What Donald Trump said disqualifies him from serving as president," said Mr Earnest, describing the remarks as "offensive" and "toxic".
Democratic frontrunner Hillary Clinton said the billionaire's comments aided terrorists.
"It's a shameful idea. It's also dangerous," she said.
"At a time when America should be doing everything we can to fight radical jihadists, Mr Trump is supplying them with new propaganda."
But Mr Trump has also earned the wrath of the United Nations
Zeid Ra'ad Al Hussein, the UN High Commissioner for Human Rights, said the comments were "grossly irresponsible".
David Cameron called Mr Trump's proposal "divisive and unhelpful", while senior politicians in France and Canada have spoken out too.
Muslim leaders in the US have also criticised the 69 year old.
"ISIS is to Islam what Donald Trump is to American values: a complete distortion of everything that we as a country and a society stand for," said Sohaib Sultan, Muslim Life Coordinator and Chaplain at Princeton University.
But in Australia, former Prime Minister Tony Abbott has been accused of "Trumpifying" Australian politics by saying the West should proclaim its superiority over Islam.
George Osborne, standing in for Mr Cameron during Prime Minister's Questions, was cautious on the question of whether Mr Trump should be banned.
He said: "I think the best way to confront the views of someone like Donald Trump is to engage him in a robust democratic argument about why he is profoundly wrong about the contribution of American Muslims and indeed British Muslims.
"That is the best way to deal with Donald Trump and his views rather than trying to ban presidential candidates."
Mr Trump was unrepentant in a series of TV interviews on Tuesday.
He compared his idea to the internment of Japanese and Germans during World War II by Franklin Roosevelt.
On the charge that he was aiding IS propaganda, he said: "I'm the worst thing that's ever happened to ISIS."