The number of people signing the petition, which was set up almost two weeks ago, soared in recent days following calls by the property tycoon and reality TV star for Muslims to be barred from entering the US and his claim that parts of London were so “radicalised” that police feared for their lives.
A poll on the parliamentary website calling for his exclusion from the UK raced past the 100,000-signature threshold to be considered for debate in Parliament and has topped the previous record of 446,482.
At its peak, the petition was lengthening by more than seven signatures a second and users experienced difficulties accessing the page due to higher than usual traffic. It gained around 140,000 signatures in just over a day, to reach the 500,000 mark in the early hours of Friday.
The previous top spot was held by a petition earlier this year calling for the UK to accept more asylum seekers and increase refugee support, which was signed 446,924 times.
Prime Minister David Cameron said Mr Trump’s comments were “divisive, unhelpful and quite simply wrong”, while London mayor Boris Johnson said they rendered him “unfit to hold the office of the president of the United States”.
The businessman, who owns two golf courses in Scotland - Trump International Golf Links in Aberdeenshire and Trump Turnberry in South Ayrshire - has been stripped of an honorary degree from Robert Gordon University in Aberdeen and had his membership of the GlobalScot business network removed.
But he received support from TV personality and MailOnline columnist Katie Hopkins, who urged the public not to demonise him.
Hopkins, who told Fox News Mr Trump had support from a quarter of the population of the UK, tweeted: “It’s because Trump & I articulate sentiments repressed by the politically correct consensus that we have a voice.”
Mr Trump then thanked the “respected columnist” for her “powerful writing on the U.K.’s Muslim problems” before claiming “Many people in the U.K. agree with me!”.
Following a backlash about his comments on police in London he remained unrepentant, writing on Twitter: “The United Kingdom is trying hard to disguise their massive Muslim problem.
“Everybody is wise to what is happening, very sad! Be honest.”
Polls taken in the US after Mr Trump’s original remarks were publicised showed a spike in support among Republican primary voters, with Mr Trump on around 35% and as many as 20 points ahead of his main rivals.
Suzanne Kelly, who originally lodged the petition to ban the US billionaire, 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 petition can be found on the UK Government website by clicking here.