Prime Minister Theresa May has told her foreign secretary and home secretary to contact their US counterparts about a travel ban imposed by President Trump.
Boris Johnson is pressing Mr Trump’s advisers to exempt Britons with dual citizenship from the 90-day ban on visa holders from seven countries .
Earlier Mr Johnson tweeted it was „divisive and wrong“ to stigmatise people on the basis of nationality.
Mrs May has come under fire for not condemning the order earlier.
A petition to stop a state visit to the UK by President Trump later this year may be debated in Parliament, after amassing more than 350,000 signatures.
The prime minister had been criticised for not condemning the US order when she was first asked about it, at a press conference in Turkey on Saturday.
She initially said it was up to the US to decide its policy on refugees but No 10 later issued a statement saying she did „not agree with this kind of approach and it is not one we will be taking“.
Downing Street said her decision to tell Mr Johnson and Ms Rudd to speak to the State Department and the Department of Homeland Security showed she was „absolutely determined“ to respond to fears about the ban.
It is understood Mr Johnson has been speaking to Mr Trump’s chief strategist Steve Bannon and senior adviser Jared Kushner about how to stop travelling Britons being affected by the 90-day travel ban for nationals from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Earlier Mr Johnson joined those speaking out against Mr Trump’s executive order, writing on Twitter: „We will protect the rights and freedoms of UK nationals home and abroad. “
A Conservative MP, Nadhim Zahawi, who was born in Iraq, is among those who have said they would not be able to travel to the US while the temporary ban is in place.
BBC political correspondent Susana Mendonca
There is a much tougher message coming from Downing Street today. Theresa May has ordered the foreign secretary and home secretary to make representations to their opposite numbers in the US government about the travel ban, and both Boris Johnson and the Chief Secretary to the Treasury David Gauke have called Mr Trump’s policy „divisive“ and „wrong“.
The British government is at pains to make it clear just how much it disagrees with this US travel ban. Theresa May’s failure to do that at a press conference in Turkey yesterday led to a backlash from MPs on all sides who had wanted to see a tougher stance – given she had promised not to be afraid to tell Donald Trump when she didn’t agree with him. That’s hard do, though, when Mrs May also needs to forge a good working relationship with the controversial new president.
Mr Gauke, defending the PM this morning, said she wasn’t the kind of politician who „shoots from the hip“; that she had to see the evidence first; and that was why she wasn’t quick to judge. Even Nadhim Zahawi MP – himself a victim of Mr Trump’s travel ban – was at pains not to criticise the PM personally.
But now the PM faces another potential problem, as a petition calling for Donald Trump not be invited for a State visit to the UK has already gained enough signatures to be considered for a debate in parliament.
British Olympic champion Sir Mo Farah, who was born in Somalia and lives in the US, has also said it is „deeply troubling“ that he may have to tell his children he cannot go home .
Labour leader Jeremy Corbyn said it would be „totally wrong“ for a proposed state visit to the UK by Mr Trump to go ahead while the row continued.
Labour’s former leader Ed Miliband said Mrs May must „get on the phone“ to the president.
„You’re the prime minister,“ he said. „Get on the phone to the president and tell him the ban cannot stand. And do it today. “
London Mayor Sadiq Khan told Sky News the UK „should not be rolling out the red carpet for President Trump“ while the travel ban was in place.
Scotland’s First Minister Nicola Sturgeon also said it should not go ahead while the order was in place.
