Don’t be surprised if Theresa May doesn’t get too upset about President Donald Trump’s travel ban, because when it comes to resiling from the international system of refugee protection she is already several steps ahead of him.

The prime minister was caught on the hop when she flew back from Turkey on Saturday night into a Twitter-storm over how a little-noticed “dual-national” element of the ban could catch Sir Mo Farah and the Iraqi-born Conservative MP for Stratford-upon-Avon, Nadhim Zahawi.

US travel ban - a brief guide The executive order signed by Donald Trump suspends the entire US refugee admissions system, already one of the most rigorous in the world, for 120 days. It also suspends the Syrian refugee program indefinitely, and bans entry to the US to people from seven majority-Muslim countries – Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen – for 90 days. The order has prompted a series of legal challenges, while thousands of Americans have protested outside airports and courthouses in solidarity with Muslims and migrants.

Downing Street rushed out a statement saying it did not agree with the ban but would make sure it did not affect any British nationals.

However, May refused to criticise – as she had done at a press conference in Turkey when asked three times about the policy – the underlying policy behind the ban.

Trump’s executive order suspends the US’s entire refugee resettlement programme – the largest in the world – for 120 days, places a temporary 90-day ban on visitors from seven predominantly Muslim countries, and an indefinite ban on the arrival of Syrian refugees.

Trump frames the policy as one of keeping the US safe from terrorism. But a quick glance at the list – Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen – shows that it clearly omits several major candidates for a US anti-terrorist “no-fly list” such as Afghanistan, Pakistan and Saudi Arabia.

This is because the list is not a top seven terrorist-producing countries list but a list of the top seven countries for producing refugees given sanctuary in the US – often fleeing state terrorism and war.

Trump has declared the aim of his policy is to cut the number of UNHCR-nominated refugees resettled in America this year from the planned 110,000 to 50,000.

Since 1980, US presidents have taken the biggest role in the UN refugee agency’s resettlement programme. It has, up to now, been seen as a crucial component of America’s national identity as welcoming the “huddled masses yearning to breathe free”.

But Trump’s adoption of temporary bans and “extreme vetting” in the name of counter-terrorism now threatens to undermine the international system of refugee protection and the global stability it helps to provide. It will also leave in limbo 60,000 UNCHR-nominated refugees who have already been through a lengthy vetting process and are now banned from entering the US.

At the heart of the matter is Trump’s rejection of the vetting process, despite the fact that those nominated by the UNHCR have to be approved by no fewer than 24 US departments and agencies before they are accepted for resettlement.

The UNHCR says it is “acutely aware” of host countries’ “entirely legitimate” concerns about the resettlement programme being used as a cover for terrorists, and adds that it uses biometric data, audit trails and an electronic registration database to ensure the integrity of its programmes.

But this is not enough for Trump. He is clearly going to substitute a US-only vetting system, further undermining trust in the UNHCR system.

Theresa May is already way past him. When David Cameron pledged Britain to take 20,000 of the most vulnerable Syrian refugees May insisted that the country would not take part in a UNHCR-run scheme. Instead, Britain set up a separate programme in which refugees nominated by the agency are vetted by Home Office officials.

May wants to go much further. In her party conference speech in October 2015, amid the world’s worst refugee crisis since the second world war, she outlined a new asylum strategy under which only temporary protection would be given to all but the world’s most vulnerable refugees. She said she was keen to see the international legal definition of a refugee made much stricter.

The prime minister may well have been embarrassed by the clumsy “dual-national” interpretation of Trump’s temporary bans that led to the prospect of Farah and Zahawi being told they were no longer welcome in the US.

Trump’s underlying policy on refugees is to undermine the accepted international system of refugee protection that has been in place since 1951. Theresa May is already ahead of him on that road.