The petition, posted on the official website of parliament, means that it will be considered for debate in the House of Commons. At one point, the petition was lengthening by more than seven signatures a second.
The property tycoon and reality TV star, who is seeking the Republican nomination for next year’s presidential election, has provoked widespread anger and ridicule after calling for a ban on Muslims entering the United States and claiming that parts of the British capital were “so radicalised” that police were “afraid for their own lives”.
Mr Trump’s comments about Islamist radicalisation in London make him “unfit” to be US president, the city’s mayor Boris Johnson has said.
But Chancellor George Osborne dismissed calls for Trump to be excluded from the UK, saying it was better for his “nonsense” views to be challenged in debate.
Downing Street has made clear that David Cameron regards the presidential hopeful’s comments as “divisive, unhelpful and quite simply wrong”.
But 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.”
Meanwhile 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.