US presidential hopeful Donald Trump has attracted widespread derision after claiming that parts of London were "so radicalised" that police were "afraid for their own lives".
David Cameron's official spokeswoman said the Prime Minister would "clearly disagree" with the would-be president, while London mayor Boris Johnson dismissed Mr Trump's "ill-informed" comments as "nonsense".
Mr Trump's outspoken statement followed his call for Muslims to be barred from entering America, a move slammed as "divisive, unhelpful and quite simply wrong" by Mr Cameron.
Speaking to MSNBC in the US, Mr Trump said: "We have places in London and other places that are so radicalised that the police are afraid for their own lives. We have to be very smart and very vigilant."
Mr Cameron's official spokeswoman said: "The Prime Minister would clearly disagree with Donald Trump and think that his views are wrong."
The Downing Street comments represent a departure from the practice usually followed by British prime ministers of avoiding commentary on the merits of contenders in the US presidential race.
Mr Johnson ridiculed the business tycoon, who is seeking the Republican nomination for next year's presidential election, saying "the only reason I wouldn't go to some parts of New York is the real risk of meeting Donald Trump".
He said: "Donald Trump's ill-informed comments are complete and utter nonsense.
"As a city where more than 300 languages are spoken, London has a proud history of tolerance and diversity and to suggest there are areas where police officers cannot go because of radicalisation is simply ridiculous.
"I would welcome the opportunity to show Mr Trump first hand some of the excellent work our police officers do every day in local neighbourhoods throughout our city.
"Crime has been falling steadily both in London and in New York - and the only reason I wouldn't go to some parts of New York is the real risk of meeting Donald Trump."
A Metropolitan Police spokeswoman said: "We would not normally dignify such comments with a response, however on this occasion we think it's important to state to Londoners that Mr Trump could not be more wrong.
"Any candidate for the presidential election in the United States of America is welcome to receive a briefing from the Met Police on the reality of policing London."
The Muslim Council of Britain offered to take Mr Trump for lunch if he visited London.
A spokesman said:" We know that Mr Trump does not represent the views of ordinary Americans, and we reject his ignorant remarks suggesting that London has no-go areas where even the police are afraid to enter.
"Should he be allowed to enter the UK, and if he is able to name such areas, we would be happy to organise a multi-faith delegation to accompany Mr Trump and tour these areas and pay for his lunch."
Mr Trump's call for a "total and complete shutdown" of Muslims entering the US came in the wake of last week's terror attack in San Bernardino, California, where a Muslim couple believed to have been radicalised shot 14 dead at a health centre.
Speaking to a regular media briefing in Westminster, Mr Cameron's official spokeswoman declined to say whether Mr Trump's comments might lead to him being barred from entry to the UK under hate-speech laws.
Campaigners against Mr Trump's golf course development in Scotland have submitted a petition to Parliament calling for him to be barred from the UK "for his continued, unrepentant hate speech and unacceptable behaviour". The petition is under consideration for inclusion on the parliamentary website.
Mr Cameron's spokeswoman declined to say whether the PM would be willing to meet Mr Trump or whether he might be blocked from entry to the UK, describing the questions as "hypothetical".
But she said: "The Prime Minister completely disagrees with the comments made by Donald Trump, which are divisive, unhelpful and quite simply wrong."
Labour leader Jeremy Corbyn said: "Trump's call to ban Muslims from entering the US is an attack on democratic values."
He said the presidential hopeful's remarks were an "affront to common humanity" and called for people to "unite against racism".
Scotland's First Minister Nicola Sturgeon said: "Donald Trump's comments are obnoxious and offensive, and have rightly been condemned by people across the political spectrum, in the United States and elsewhere.
"Mr Trump's views are repugnant, and they clearly do not represent the mainstream views of people across America."