Sadiq Khan today predicted Donald Trump would lose the White House race in November as he continued a war of words with the Republican nominee over his policy on Muslims.

The billionaire tycoon reignited the row today by claiming Mr Khan was 'ignorant' about his policy to stop Muslims entering America until the threat from terrorism was understood - and even suggested London's new Mayor should take an IQ test.

But Mr Khan immediately hit back at the presumptive Republican nominee, branding him 'nasty and rude' and warning his 'politics of fear' would fail at the ballot box as surely in America as it had in London.

Mr Trump's latest intervention on British politics came in an interview with Piers Morgan for ITV's Good Morning Britain.

Angry: Donald Trump told Piers Morgan today that London Mayor Sadiq Khan is 'ignorant' and said he should take an IQ test

Mr Khan, who was mobbed by Londoners wanting selfies this morning, hit back at Mr Trump to warn ignorance was not the same as intelligence

The White House contender also warned the special relationship could be in danger if David Cameron continued to refuse to apologise for dubbing him 'stupid, divisive and wrong'.

Downing Street today said Mr Cameron would continue to stand by his remarks and had not changed his view that blocking Muslims from entering America was the wrong thing to do.

Mr Khan said while campaigning that he would be banned from America if Mr Trump was elected.

He said that Trump's comments 'plays into the hands of the extremists' and called him 'ignorant'.

Today the hotel mogul responded by saying: 'When he won I wished him well. Now, I don't care about him, I mean it doesn't mean any difference to me, let's see how he does, let's see if he's a good mayor.'

Mr Trump continued: 'He doesn't know me, hasn't met me, doesn't know what I'm all about.

'I think they were very rude statements and, frankly, tell him I will remember those statements. They are very nasty statements.'

Asked if he was offended by Mr Khan's public denouncement he replied: 'Yeah, I am.'

A spokesman for Mr Khan rejected the new intervention.

He said: '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.'

Targets: Mr Trump has criticised David Cameron and Sadiq Khan in a new interview and also said Britain should leave the EU

The spokesman continued: '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.'

Asked if Mr Khan would take up the offer of an IQ test, the spokesman said: 'Ignorance is not the same thing as a lack of intelligence.'

In other remarks, Mr Trump also weighed in to the EU referendum battle and said the UK should leave because: 'What do you need it for?'

Asked whether Mr Cameron was concerned about Mr Trump's suggestion that they might not have a good relationship, a Downing Street spokesman said: '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 Number 10 spokesman said that Mr Cameron was 'committed to maintaining the special relationship' whoever wins the presidential election.

'He has been clear that he will work with whoever is president of the United States,' said the spokesman.

No proposal had been made for a phone call between the PM and Mr Trump, but Downing Street would be willing to consider it, the spokesman added.

Mr Trump has been in a war of words with British politicians since December when he called for 'a total and complete shutdown of Muslims entering the United States'

The billionaire's statement after the killing of 14 people by two ISIS sympathisers in California were branded 'stupid' and 'divisive' by Mr Cameron.

He told Mr Morgan that he might struggle to get on with the Prime Minister if he is elected president.

He said: 'It looks like we're not going to have a very good relationship, who knows, I hope to have a good relationship with him but it sounds like he's not willing to address the problem either'.

Controversial: The Republican nominee made his latest incendiary claims about Mr Khan in an interview with ITV's Good Morning Britain

In today's interview, Mr Trump denied he was 'at war' with Mr Khan but said: '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... I think it's ignorant for him to say that.'

The United States is Britain's closest ally and political leaders from both nations often speak of how the countries' enjoy a special relationship.

Cameron earlier this month refused to retract his 'divisive, stupid and wrong' comment but said that Trump deserved respect for making it through the gruelling Republican primary process.

Mr Trump was asked if he wanted to retract his proposed ban on Muslims.

'We have a tremendous problem with radical Islamic terror,' he said.

'The world is blowing up and its not people from Sweden that's doing the damage okay. So we have a real problem.'

He also weighed in to the EU battle and said: 'What do you need it for?'

He added: 'I've dealt with the European Union, it's very very bureaucratic, it's very very difficult. But again, let people make up their own mind.'

Anti-Brussels: He also weighed in to the EU battle and said: 'What do you need it for?'

Mr Trump sparked a huge row when he announced his policy on a temporary ban on Muslims entering the United State.

He said: 'Until we are able to determine and understand this problem and the dangerous threat it poses, our country cannot be the victim of horrendous attacks by people that believe only in jihad.

'We should definitely disallow any Muslims from coming in. Any of them. The reason is simple: we can't identify what their attitude is.'

Mr Trump used the terror attacks in Paris to bolster his argument, saying: 'They have sections in Paris that are radicalised, where the police refuse to go there. They're petrified. The police refuse to go in there.'

He added: 'We have places in London and other places that are so radicalised that police are afraid for their own lives.'

Mr Trump currently trails in most opinion polls behind his likely Democrat rival Hillary Clinton ahead of November's general election

The Home Secretary joined David Cameron and Boris Johnson in criticising Mr Trump but some serving police officers told MailOnline he was right.

The proposal provoked outrage and inspired the then largest biggest petition to Parliament demanding Mr Trump be banned from Britain.

The Government refused to endorse the petition directly but several senior politicians, led by Mr Cameron, took the opportunity to enthusiastically condemn the then outsider for the White House.

In the same Piers Morgan interview Mr Trump said a post-Brexit UK would not be sent to the back of the queue to secure a trade deal with the US should he become president.

His comments contradict those of President Barack Obama who on a visit to Downing Street warned last month that Britain would be 'at the back of the queue' in terms of a trade deal. Mr Trump repeated his opinion that the UK should leave the EU and said: 'I think if I were from Britain I would probably want to go back to a different system.'

Asked if the UK would be at the front of the queue for a trade deal under a Trump presidency, he replied: 'I don't want to say front or anything else. I mean, I'm going to treat everybody fairly but it wouldn't make any difference to me whether they were in the EU or not.'

He added: 'You'd certainly not be back of the queue, that I can tell you.'