By Wednesday afternoon, the "Block Donald J Trump from UK entry" petition had been signed by more than 250,000 people.
Having received more than 100,000 signatures, the petition now has to be considered for debate by parliament and will require a written government response.
"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 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."
The petition was launched in response to a call made by the 69-year-old presidential hopeful to ban Muslims from entering the US earlier this week.
On Monday, the former reality television host called for a "total and complete" block on Muslims entering the US "until our country's representatives can figure out what is going on".
His comments were widely condemned by politicians and officials worldwide, including the British Prime Minister David Cameron, who said Trump's comments were "divisive, unhelpful and quite simply wrong".
Chancellor George Osborne said that while Trump's comments "fly in the face of the founding principle of the United States ... the best way to defeat nonsense like this is to engage in robust democratic debate" - not by placing a ban on his travel.
Meanwhile, Jeremy Corbyn, the leader of the opposition Labour party, tweeted: "Trump's call to ban Muslims from entering the US is an attack on democratic values & affront to common humanity. Let's unite against racism".
Meanwhile, the Robert Gordon University in Aberdeen, UK, revoked an honorary degree issued in 2010 because "Mr Trump has made a number of statements that are wholly incompatible with the ethos and values of the university".
