The 'Block Donald J Donald Trump From UK Entry' Petition will now be considered for a debate in the Commons after garnering more than 350,000 signatures by Thursday morning.
In just one day, hundreds of thousands of people signed the petition in reaction to Trump's declaration that he wants to ban all Muslims from entering the US.
At one point, the petition was lengthening by more than seven signatures a second.
Once a petition tops 100,000 signatures it must be considered for debate in parliament - although there is no promise that it will actually go ahead.
A statement on the petition read: "The UK has banned entry to many individuals for hate speech. The same principles should apply to everyone who wishes to enter the UK.
"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."
On Wednesday, George Osborne, standing in for David Cameron at Prime Minister's Questions said Trump will not be banned from the UK despite talking "nonsense".
He said that instead, Trump's critics should "engage in a robust democratic argument with him" when urged by MP Tasmina Ahmed-Sheikh to make him the 85th "hate preacher" banned by Home Secretary Theresa May.
Cameron has already spoken out against Trump's comments.
The Prime Minister's official spokeswoman said: "The PM completely disagrees with the comments made by Donald Trump which are divisive, unhelpful and quite simply wrong," a spokesman for Downing St said on Tuesday.
"The PM is clear that as we look at how we tackle extremism and this poisonous ideology, what politicians need to do is look at ways they can bring communities together and make clear these terrorists are not representative of Islam, indeed what they are doing is a perversion of Islam."
Pressure has also been placed on May by think-tank, British Future, to ban Donald Trump from the UK.
Sunder Katwala, British Future director, said on Tuesday the Home Secretary should consider blocking any attempt by Trump to visit Britain in response.
"Donald Trump’s call for a blanket ban on Muslims visiting America represents a real low in electoral politics. It is hugely irresponsible for a prominent figure like Trump to fan the flames of prejudice in this way," he said in a statement.
"The UK Home Office has set out clear guidelines which have led to the exclusion of preachers of hate from the UK if their presence here would not be conducive to the public good.
"Theresa May has excluded extreme Islamists on these grounds, and also kept out those who have fanned extreme anti-Muslim prejudice, such as the bloggers Pamela Geller and Robert Spencer. Trump’s statements are more extreme than theirs."
London Mayor Boris Johnson today said that Trump's comments about Islamist radicalisation in the city make him "unfit" to be US president.
Mr Johnson is the first prominent British politician to suggest they render Mr Trump unfit for office.
The mayor told ITV News: "I think Donald Trump is clearly out of his mind if he thinks that's a sensible way to proceed. You can't ban people going to the US in that way, or indeed to any country.
"What he's doing is playing the game of the terrorists and those who seek to divide us. That is exactly the kind of reaction they hope to produce.
"When Donald Trump says there are parts of London that are no-go areas, I think he is betraying a quite stupefying ignorance that makes him frankly unfit to hold the office of the president of the United States."
Mr Johnson joked: "I would invite him to come and see the whole of London and take him round the city, except that I wouldn't want to expose Londoners to any unnecessary risk of meeting Donald Trump."
The property tycoon is currently the frontrunner in the Republican presidential candidate race.
Although known for his controversial views, many people believe that he has gone too far with his latest suggestion to close US borders to Muslims following the San Bernardino terrorist attack last week.
Even Trump's friend, Piers Morgan, has spoken out against Trump's divisive comments, saying yesterday that he has "crossed a line".