David Cameron should snub Donald Trump or criticise the controversial Republican presidential nominee to his face, according to a new poll.

Just one in four people back the traditional diplomacy that might be expected from a meeting between the Prime Minister and a potential American President.

Mr Cameron said last week that he would be “very happy” to meet Mr Trump, who has been accused of racism and sexism in his race to secure his party’s vote.

The Prime Minister, who four years ago posed with the then Republican candidate Mitt Romney inside Downing Street, also insisted that the UK’s ‘special relationship’ with America would continue even if Mr Trump became President.

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But a new UK-wide poll by BMG for The Herald shows that the public is deeply divided over whether or not Mr Cameron should meet the outspoken tycoon.

Overall, more than 4 in 10 people, 42 per cent, do not think the Conservative leader should host Mr Trump.

One in five, 22 per cent, believe he should “intentionally snub” him.

Another 31 per cent want the two men to meet – but only so that Mr Cameron can attack Mr Trump face-to-face.

The Herald:

Just over one in four, 27 per cent, back an uncontroversial meeting.

The Herald revealed last week that Mr Trump is due to fly into Scotland – and into a barrage at protests– at the end of next month.

The news has prompted speculation that he could try to see Mr Cameron on the same trip.

The New York billionaire attracted global condemnation when he called for a " total and complete shutdown of Muslims entering the United States" after a Muslim couple, believed to have been radicalised, opened fire and killed 14 people at a health centre in San Bernardino, California.

Read more: David Cameron insists Trump deserves "respect" for his battle through US presidential primaries

He has also been criticised for his claims that women should be punished if they have an abortion and that Mexico should be forced to pay to build a wall on its border with America.

His comments about Muslims led to calls from SNP politicians and others for Mr Trump to be barred from the UK for hate speech.

Mr Cameron has repeatedly said that Mr Trump’s comments around Muslims were divisive and wrong.

The Herald:

But critics said that Mr Trump’s views must not be condoned through a meeting with the Prime Minister.

Liberal Democrat leader Tim Farron said that the poll results showed that when a “reality star spouts hatred to get ahead, the British people turn their backs”.

He added that while the Prime Minister must keep an “open dialogue” with America, but “ to maintain such an historically warm relationship with a President Trump would be impossible."

Read more: David Cameron orders diplomatic offensive with Donald Trump - just in case

Michael Turner from BMG said that the findings “highlight just how difficult international diplomacy can be today. The results suggest that if Cameron were to actually meet with Mr Trump, it would be interpreted in many different ways. People are genuinely divided on how best to tackle both a presidential nominee, and a man whose views are often described as offensive.”

Last week Mr Cameron stopped short of congratulating Mr Trump for securing his party’s nomination.

He did however congratulate the former presenter of the American version of The Apprentice on what he said had been an “extraordinary” campaign marathon.

The Prime Minister would also not be drawn on previous remarks that a visit by Mr Trump to the UK “would unite us all against him”, adding that he would be willing to meet the businessman.

Campaigners are planning to disrupt Mr Trump’s visit to Scotland, which has been timed to coincide with the re-opening of Trump Turnberry after a £200 million refurbishment.

Earlier this year police were called to Mr Trump’s Aberdeenshire golf resort following a protest.