"The UK has banned entry to many individuals for hate speech. The same principles should apply to everyone who wishes to enter the UK," read the petition, which was created by Suzanne Kelly, a woman from Aberdeen, Scotland, who has previously campaigned against Trump's political and business activities.
"If the United Kingdom is to continue applying the 'unacceptable behavior' 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 stated.
By Wednesday evening, the petition had gained more than 300,000 signatures, with the number climbing rapidly.
Any petition that gets more than 100,000 signatures is considered by Parliament's Petitions Committee, which weighs whether to send the petition for debate by lawmakers in Parliament.
The committee will consider what to do with the petition on January 5, according to the House of Commons information office.
The Home Office told CNN that the home secretary has the power to exclude individuals, but there is currently no suggestion that this would be the case with Trump.
Kelly, who writes for a citizen journalist website, Aberdeen Voice, has previously written reports documenting issues with Trump's development of a high-end golf resort in Aberdeen
, which saw him come into conflict with locals.
She had earlier started a petition
asking Aberdeen's Robert Gordon University to strip Trump of an honorary degree it bestowed on him five years ago.
That petition, which attracted more than 38,000 signatures, argues that Trump's "unrepentant, persistent verbal attacks on various groups of people based on nationality, religion, race and physical abilities are a huge detriment" to the university.
Kelly wrote on the Aberdeen Voice website
that her latest petition, to ban Trump from the UK, would allow British residents "who want to stand up against hate speech ... the opportunity to do so."
"We are looking at a US Presidential candidate who wants to institute policies which to me are fascism," she wrote. "People have been barred from the United Kingdom for less."
Trump's remarks prompted outrage at home and internationally
. White House press secretary Josh Earnest said the comments effectively "disqualifies him from serving as president."
His followup remarks a day later -- that parts of London were so radicalized that British police feared for their lives -- particularly rankled in the UK.
British Prime Minister David Cameron
, who doesn't usually comment on U.S. presidential candidates, said through a spokesman that Trump's comments were "divisive, unhelpful and quite simply wrong."
London's Metropolitan Police issued a statement inviting the Republican candidate to a briefing "on the reality of policing London," while the remarks also drew a sharp response from London Mayor Boris Johnson
"Donald Trump's ill-informed comments are complete and utter nonsense," Johnson said. "The only reason I wouldn't go to some parts of New York is the real risk of meeting Donald Trump."
But his comments may also have found some sympathizers in a country wary of the ISIS threat. Another petition on the UK government website
calls on British leaders to "stop all immigration and close the UK borders until ISIS is defeated."
That petition, which cited ISIS threats to send jihadists to Europe among refugees, has gathered more than 440,000 signatures since it was launched in September, but was rejected by the British government.
"The UK government has no intention of closing Britain's borders, as this would create more problems than it would solve," the British Home Office wrote in rejecting the proposal.