More than 1 million people have signed an online petition calling for US President Donald Trump's planned state visit to Britain to be cancelled to avoid embarrassing Queen Elizabeth II.

The petition was created before Mr Trump barred Syrian refugees and suspended travel from seven Muslim-majority countries, but gained almost immediate traction after the President signed his executive order.

It rose from less than 100 signatures, which it had sat at for eight weeks, to stand at more than 1.5 million this morning (AEST).

But British Prime Minister Theresa May's office shut down the idea of a cancellation, saying the visit would go ahead as planned.

The invitation to make a state visit, which will involve lavish displays of royal pageantry and a banquet hosted by the monarch, was conveyed by Ms May when she visited Mr Trump last week.

Mr Trump's executive order bans travel for seven majority Muslim countries — Iran, Iraq, Somalia, Syria, Sudan, Libya and Yemen — for 90 days, suspends all refugee admissions for 120 days with case-by-case exceptions and suspends entry of Syrian refugees indefinitely.

Second most popular parliamentary petition ever

The petition, created by Leeds man Graham Guest, asserted that such a visit would "cause embarrassment" to the Queen.

"Donald Trump should be allowed to enter the UK in his capacity as head of the US Government, but he should not be invited to make an official state visit," the petition reads.

"Donald Trump's well-documented misogyny and vulgarity disqualifies him from being received by Her Majesty the Queen or the Prince of Wales.

"Therefore, during the term of his presidency Donald Trump should not be invited to the United Kingdom for an official state visit."

Mr Guest told The Independent that Mr Trump's executive order "changes things slightly".

"It's added a new dimension to things and until that ban is lifted I don't think he should come to the country at all in any capacity," he said.

The number of signatures on the petition continues to rise rapidly. ( Supplied: UK Government and Parliament )

It has become the second most popular petition ever on the parliamentary website, after one calling for a second referendum on membership of the European Union drew over 4 million signatures last year.

Once a petition passes 100,000 signatures, politicians must consider it for debate, and although such debates were largely symbolic and rarely affected government policy, this particular one would potentially be embarrassing for Ms May.

Ms May's Downing Street office said "an invitation has been extended and accepted" but declined to comment any further.

A year ago, parliament debated a petition calling for Mr Trump, then the Republican candidate, to be barred from the UK.

It gathered close to 600,000 signatures before it was closed last June.

Some politicians from the governing Conservative Party and opposition Labour Party have criticised Mr Trump's immigration order, with Labour leader Jeremy Corbyn saying the state visit should be put on hold.

Protesters out in force throughout UK

Tens of thousands of people protested in London and other cities against Mr Trump's immigration ban.

Sorry, this video has expired Boris Johnson labels US travel ban 'divisive and wrong'

Thousands of people, some holding placards reading "No to Racism, No to Trump", "Dump Trump" and "I stand with Muslims", joined a protest on Monday outside the Downing Street residence of Ms May.

Some chanted "Shame on May" for her offer to Mr Trump of a visit to Britain.

"It's a lot worse under Trump than I was expecting, because it's only been 10 days but he's changed so much already," Rawnak Jassm, a 23-year-old British-Iraqi, who joined the protest, said.

"It's pretty scary."

Mr Trump's immigration crackdown and the subsequent backlash has seen British parliament embroiled in fierce debates.

Outspoken Labor MP Dennis Skinner was among those who said the UK has to stand up to the US President, saying the country should "do the decent thing" and ban Mr Trump's visit.

British Foreign Secretary Boris Johnson was critical of the immigration ban, calling it "divisive, discriminatory and wrong", but was adamant the visit of Mr Trump would not be postponed.

"He is the elected head of state of our closest and important ally," Mr Johnson said.

Tens of thousands of people protested in London and other cities against Mr Trump's immigration ban. ( Supplied: Kate Muffet )

ABC/wires