DOWNING Street has indicated that Britain’s special relationship with America would continue if Donald Trump became the 45th US President.

The declaration came after the presumptive Republican nominee, noting David Cameron’s previous comments about his views on Muslims, said: “It looks like we are not going to have a very good relationship. Who knows, I hope to have a good relationship with him but he's not willing to address the problem either."

The Prime Minister’s spokesman, asked if Mr Cameron believed the special relationship would continue whoever became president, replied that the PM was "committed to maintaining the special relationship". Asked if that meant whoever was in the White House, he replied: “Yes.”

The spokesman stressed "He has been clear that he will work with whoever is president of the United States."

Asked whether Mr Cameron was concerned about Mr Trump's suggestion that they might not have a good relationship, he replied: "The Prime Minister has made his views on Donald Trump's comments very clear. He disagrees with them, and I haven't got anything further to add. He continues to believe that preventing Muslims from entering the US is divisive, stupid and wrong."

The spokesman said no proposal had been made for a phone call between the PM and Mr Trump but, he added, No 10 would be willing to consider it.

Meantime, Sadiq Khan, the new London mayor, claimed US voters would reject Mr Trump because his "ignorant, divisive and dangerous" views played into the hands of extremists.

The public spat between the new Labour mayor and the billionaire businessman resumed after Mr Trump called the prominent Muslim politician "ignorant" and "nasty" in an interview with ITV's Good Morning Britain.

A spokesman for the mayor hit back, saying: "Donald Trump's views are ignorant, divisive and dangerous - it's the politics of fear at its worst and will be rejected at the ballot box just as it was in London.

"Sadiq has spent his whole life fighting extremism, but Trump's remarks make that fight much harder for us all - it plays straight into the extremists' hands and makes both our countries less safe."

He said there were "no plans" to seek direct talks and mocked Mr Trump's challenge to the mayor to take an IQ test.

"Ignorance is not the same thing as lack of intelligence," added the spokesman.

Mr Trump's campaign call for a temporary ban on Muslims entering the US led to almost universal condemnation from UK politicians, including Mr Cameron, who called it "divisive, stupid and wrong".

Asked about potential future trans-Atlantic tensions if he became president, the tycoon told GMB: "It looks like we are not going to have a very good relationship.”

Mr Trump had appeared to offer an olive branch to Mr Khan after his election to City Hall - in the face of a Conservative campaign critics compared with the Republican's aggressive tone - saying there would "always be exemptions" to the ban.

But he pointedly said he would "remember" the hostile reaction that he received from the mayor, who said his own election had shown voters would not back "divisive" candidates.

"He doesn't know me, hasn't met me, doesn't know what I'm all about," declared Mr Trump. "They were very rude statements and, frankly, tell him I will remember those statements. They are very nasty statements," the Republican nominee told GMB.

"When he won I wished him well. Now, I don't care about him, I mean, it doesn't make any difference to me, let's see how he does, let's see if he's a good mayor."

Mr tycoon said he was offended by Mr Khan's public denouncement but denied he was "at war" with him.

"I just think it's very rude of him. In fact it's the opposite. I wished him well when I heard he won; he's a Muslim, it's ignorant for him to say that."

The presidential hopeful said the policies he mooted on the campaign trail were just "suggestions" but said there was a "tremendous" problem with Islamic extremism.

"It's not Sweden doing the damage; we have a real problem and we have to discuss it."

Mr Trump went on: "Number one, I'm not stupid, OK? I can tell you that right now; just the opposite. Number two...I don't think I am a divisive person; I am a unifier, unlike our president now, I'm a unifier."

The billionaire businessman claimed to have many Muslim friends. “I was with one the other day, one of the most successful men, he's Muslim and he said: 'Donald you have done us such a favour, you have brought out a problem that nobody wants to talk about.'"

Rejecting claims he was anti-Muslim, he told interviewer Piers Morgan: "Absolutely not. I am anti-terror. There's something going on that's not good, there's something going on that's very bad, there's something that you are not understanding and maybe the mayor of London is not understanding."

Elsewhere, George Osborne said he and Mr Cameron stood by their comments in response to Mr Trump's views on Muslims.

However, the Chancellor added: "But he is an American presidential candidate and we will talk to him because it is in our interest to talk to our allies like the United States."