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UK Prime Minister Theresa May has ordered ministers to press US officials about a ban on passport holders from seven Muslim-majority countries, a decision which has sparked outrage in Britain.

May, who was the first world leader to visit President Donald Trump on Friday, at first refused to condemn the move before offering a tougher rebuke.

The decision has seen her come under fire from British people and UK media who view the response from the government as weak and undignified.

But with high-profile citizens drawn into the president's border clampdown, May has been forced to move against her budding post-Brexit trading partner.

Downing Street said May does "not agree" with the restrictions and had asked senior ministers to contact their US counterparts to manage the diplomatic fallout from the controversial move.

Among the celebrities worried about the move is the UK's Somali-born double-double Olympic gold medal athlete Mo Farah. His family are US-based and saw him slam the policy, sparking applause and shares from social media users in the UK.

"On January 1 this year, Her Majesty The Queen made me a Knight of the Realm. On January 27, President Donald Trump seems to have made me an alien," wrote the athlete, who represents Britain but was born in Somalia.

An Iraqi-born MP from May's Conservative Party had earlier revealed he would be barred from entering the US under the clampdown.

Nadhim Zahawi said he had "confirmation that the order does apply to myself and my wife as we were both born in Iraq," despite bothing holding UK passports.

"A sad, sad day to feel like a second class citizen! Sad day for the USA," he added.

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Meanwhile the opposition Labour Party led by embattled Jeremy Corbyn has taken advantage of the popular mood to call for Trump's planned state visit to the UK to be frozen until the Muslim ban ends.

On the ropes, May has asked pro-US Foreign Secretary Boris Johnson and interior minister Amber Rudd to respond to the outcry at home.

They have been asked "to make representations to their opposite numbers in the State Department and the Department of Homeland Security, with the aim being to protect the rights of British nationals", said Downing Street.

It comes after May repeatedly refused to condemn Trump's executive order banning millions of Muslims when pressed by journalists during a trip to Turkey.

She only spoke out against the ruling once it emerged that British citizens had been affected.

"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," a spokesman from her office said on Sunday.

"But we do not agree with this kind of approach and it is not one we will be taking. If there is any impact on UK nationals then clearly we will make representations to the US government about that."

Johnson, who had previously warmed to Trump's election win, said the US decision was "divisive and wrong to stigmatise because of nationality".

UK leaders might also be embarrassed that Trump signed the executive order to ban millions of Muslims just hours after May's visit to the US.

An online petition calling for Trump not to be invited "because it would cause embarrassment to Her Majesty the Queen" has passed 400,000 signatures, meaning it will be considered for debate in parliament.

Agencies contributed to this story.