The president is facing stiff opposition as tens of thousands of people sign the online petition urging the British government to block him from visiting the UK.
It comes in the wake of Mr Trump's controversial move to ban people from mainly Muslim countries from travelling to the US.
The number of signatures -over 100,000- almost certainly means that Parliament will have to be debated in Westminster Hall.
Donald Trump is facing stiff opposition to his visit to the UK due to his Muslim ban
The petition says "he should not be invited to make an official State Visit because it would cause embarrassment to Her Majesty the Queen".
It was created in response to Mr Trump's executive order to enforce a Muslim ban.
The ban came into affect on Friday to prevent people from mainly Islamic countries from entering America.
US border control must now turn travellers away from Syria, Iraq, Sudan, Iran, Libya, Yemen and Somalia over the next 90 days.
Syrian refuges have been banned from the country indefinitely.
The petition has garnered thouands of signatures
The online petition received over 100,000 signatures in just a few minutes.
By 12.45pm on Sunday, it had enough signatures to be discussed in parliament.
Most of the people who signed the petition came from North, South, and Central London, and Brighton, Bristol, Edinburgh and Manchester.
President Trump signed the executive order against Muslim travellers on Friday
Just before midnight on Saturday, a spokesperson for Ms May said she oposed the ban.
She said: "Immigration policy in the United States is a matter for the government of the United States, just the same as immigration policy for this country should be set by our government."
However, Downing Street added that Mr Trump's state visit is still set to go ahead in June.
But, this, it seems, cannot stop the rising tide of opposition growing in the UK against Mr Trump's anti Muslim views.
Labour leader Jeremy Corbyn called for Mr Trump's visit to be cancelled unless the ban is lifted.
He told ITV's Robert Peston: "I think we should make it very clear that we are very upset about it, and it would be totally wrong for him to be coming here while that situation is going on. I think he has to be challenged on this.
"I’m not happy with him coming here until that ban is lifted, quite honestly. Look at what’s happening with those countries, how many is it going to be? And what’s going to be the long-term effect of this on the rest of the world?"
London Mayor Sadiq Khan, a Muslim, has blasted the US president's controversial ban
London's first Muslim mayor Sadiq Khan has also slammed the ban as "cruel and shameful."
He told Sky News: "We’ve already seen the consequences of this ban. A Conservative MP banned from going to America. A decorated athlete banned from going to America.”
"Our Prime Minister should not be condoning this. This is the wrong message to send out at this time when refugees need safe havens. The USA has always been a safe haven.”
“I’m pleased the Prime Minister has now said she and the government do not agree with President Trump’s policy, which will affect many British citizens who have dual nationality, including Londoners born in countries affected by the ban.
“As a nation that, like the USA, values tolerance, diversity and freedom, we cannot just shrug our shoulders and say: ‘It’s not our problem’.”
Mr Khan would not say whether he would boycott a visit of the US president if he came to London.
But he added: “I think a state visit when this type of ban is in place is wrong. We should not roll out the red carpet for this man. I don’t think he should be invited.”
Sir Mo Farah has blasted Trump's ban on Muslims from the US
Meanwhile British athlete Sir Mo Farah, who was born in Somalia, one of the banned countries, has also spoken out against the Muslim ban.
The runner has been training in Ethiopia, and, following the ban, could be stopped from returning to his home in Portland, Oregon where his wife and daughters live.
Mr Farah is Britain's most successful athlete who won double Olympic gold medals in 2012 and 2016.
He said: "I am a British citizen who has lived in America for the past six years – working hard, contributing to society, paying my taxes and bringing up our four children in the place they now call home.
"Now, me and many others like me are being told that we may not be welcome.
"It's deeply troubling that I will have to tell my children that Daddy might not be able to come home – to explain why the President has introduced a policy that comes from a place of ignorance and prejudice."
The US President faced similar calls to be banned from Britain last year – while he was the Republican nominee for president.
The debate was generated by another online petition which got nearly 574,000 signatures.
British politicians discussed banning Mr Trump in January 2016 from entering the UK, but agreed the move would "go against free speech."
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