Hundreds of thousands of people rushed to sign after Mr Trump suggested Muslims should be barred from the US.
More than 400,000 people have backed the “Block Donald J Trump from UK entry” call, with more than six signatures per second at its peak, and it is on track to beat the current record of 446,482 signatures on a petition calling for the UK to accept more asylum seekers and increase refugee support.
Suzanne Kelly, who originally lodged the document, said it was “one of many little acts of defiance” against Mr Trump.
The 54-year-old from Aberdeen said: “I started the petition on 28 November. It was after the petition was lodged that Mr Trump made his anti-Muslim remarks. These confirmed for me that what I did in starting this petition was right.
“Is there a group this man hasn’t made hateful remarks about? In a presidential candidate, this is unacceptable.
“For me freedom of speech comes with responsibility. There is great power in words, which the UK government recognises in its anti-hate speech principles. I am gratified so many people feel as I do.”
The surge in signatures came as British politicians lined up to condemn the property tycoon and reality TV star’s remarks.
Mr Trump provoked widespread anger and ridicule after demanding a block on Muslims entering the US and claiming parts of London were “so radicalised” that police were “afraid for their own lives”.
Downing Street has made clear that David Cameron regards the Republican presidential hopeful’s comments as “divisive, unhelpful and quite simply wrong”.
Chancellor George Osborne branded them “nonsense”, but dismissed calls for Mr Trump to be excluded from the UK, saying it was better for his views to be challenged in debate.
London mayor Boris Johnson said Mr Trump was unfit for office.
“I think Donald Trump is clearly out of his mind if he thinks that’s a sensible way to proceed,” he said.
“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.”
Scottish First Minister Nicola Sturgeon stripped Mr Trump of his membership of the GlobalScot business network, saying that he was no longer fit to act as a business ambassador for Scotland.
He has also been relieved of his honorary degree from Robert Gordon University (RGU) in Aberdeen, where he was awarded a doctorate of business administration in October 2010, following a separate petition set up by Ms Kelly on campaigning website 38 Degrees.
The call for Mr Trump to be barred from the UK will now be considered for debate by MPs in the House of Commons, having exceeding six-figure support.
The petitions committee is not due to meet again until January 5.