British Prime Minister Theresa May does 'not agree' with the restrictions on immigration imposed by US President Donald Trump.

London: British Prime Minister Theresa May does "not agree" with the restrictions on immigration imposed by US President Donald Trump and will intervene if they affect UK nationals, Downing Street said on Sunday.

"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 said.

"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."

May had sparked controversy in Britain on Saturday after refusing to condemn the order by Trump to suspend refugee arrivals, saying Washington was responsible for its own immigration policy.

"The United States is responsible for the United States' policy on refugees. The United Kingdom is responsible for the United Kingdom's policy on refugees," May said at a news conference during a trip to Ankara.

Meanwhile, an MP from May's Conservative Party on Saturday revealed he would be barred from entering the US under Trump's clampdown.

Iraqi-born MP Nadhim Zahawi tweeted that he had had "confirmation that the order does apply to myself and my wife as we were both born in Iraq," even though the pair have British passports.

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

The first foreign leader to meet Trump since his arrival in the White House, May discussed with the new president the possibility of quickly putting in place a trade agreement between the two countries after Britain's exit from the EU.

Shortly after their meeting on Friday, Trump signed an executive order to suspend refugee arrivals and impose tough new controls on travellers from seven Muslim countries, including Iraq, Iran, Libya, Somalia, Syria, Yemen and Sudan.

The implications for British citizens led to increasingly loud calls from lawmakers that she denounce the policy.

Tory MP Sarah Wollaston called Trump "a sickening piece of work" and demanded that he not be allowed to address both of Britain's Houses of Parliament when he makes a state visit later in the year, when he will be hosted by Queen Elizabeth II.

Opposition Labour MP Yvette Cooper said that May's refusal to condemn Trump "shames Britain".