They were given the order by Theresa May following global criticism of the US President’s executive order on immigration.
Downing Street has said that the Prime Minister does “not agree” with the controversial measures.
Mr Johnson and Ms Rudd were told to speak out over the block on refugees and many Muslims.
No 10 is particularly concerned about the impact the ban could have on UK nationals, including Iraqi-born Tory MP Nadhim Zahawi and Somali-born Olympic champion Sir Mo Farah.
The move showed how seriously the Prime Minister was taking the issue and she was “absolutely determined” to respond to the fears of Britons over the ban, No 10 sources said.
The American leader has imposed a temporary travel ban on refugees and citizens from seven mainly-Muslim countries coming to the US.
Mr Trump’s sweeping order for “extreme vetting” means no visas are being issued for 90 days to migrants or visitors from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Britons with dual nationality will also be affected, and there are concerns that UK passport holders born in those countries may also be banned.
Mr Zahawi, the Conservative MP for Stratford-on-Avon, said his sons, who were born and grew up in the UK, were due to visit from Princeton University, where they are studying, and he fears they will not be allowed to go back.
“I hope President Trump will reconsider,” he said. “Daesh (Islamic State) will be loving this day because if the leader of the free world can act in this way, then why shouldn’t they preach hatred and violence.”
Four-time Olympic champion Sir Mo says he fears the travel ban means he may not be able to return to his family in the United States.
Mr Johnson earlier tweeted it was “divisive and wrong to stigmatise” people because of their nationality as he vowed to protect Britons’ rights and freedoms.
It is not known who he will speak to as Mr Trump’s choice for Secretary of State, Rex Tillerson, has not been formally approved by the full Senate.
It comes as pressure has been mounting on Mrs May to cancel a planned state visit to the UK by President Trump later this year because of his controversial immigration policies.
A UK online petition calling for the state visit to be scrapped as it “would cause embarrassment to the Queen” has already been backed by more than 300,000 people.
Conservative leader in Scotland, Ruth Davidson, said the state visit should not go ahead as long as the “cruel and divisive” ban was in place as she urged the US leader to reconsider the policy.
Liberal Democrat leader Tim Farron told Sky News’ Sophy Ridge on Sunday that the Prime Minister should not have made the offer to the American leader and it should be withdrawn.
SNP leader Nicola Sturgeon also voiced her opposition to the state visit, while Labour leader Jeremy Corbyn suggested it should be postponed.
Sadiq Khan, London’s first Muslim mayor, called the travel ban “cruel and shameful” and while it was in place “we should not be rolling out the red carpet for President Trump”.
The Muslim Council of Britain urged the UK Government to “stand up for British values” as it condemned the ban.
There have been protests at a number of US airports against the strict controls which Mr Trump says are needed to fight international terrorism.
Read more:
:: Mo Farah – Trump seems to have made me an alien
:: Trump’s travel ban leaves passengers stranded
:: Fear and dismay of travellers hit by US bar
:: In pictures: Protests over Trump’s travel ban
:: John Legend: America ‘has to be better’ than Trump
:: Executive powers: What Trump can and can’t do
:: President Trump: His first week in office
Article source: http://news.sky.com/story/britain-to-call-us-over-president-trumps-travel-ban-10747719
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