Foreign Secretary Boris Johnson said "all British passport holders remain welcome to travel to the US".
In an address to the House of Commons, he added: "This executive order will make no difference to any British passport holder, irrespective of their country of birth or whether they hold another passport.
"This is of course a highly controversial policy, which has cause unease and I repeat, this is not an approach that this Government would take."
ITV News has travelled to Michigan, which has a large Muslim population, and spoke to residents about the divisive visa crackdown.
Thousands of people have taken to the streets across the UK to protest against Donald Trump's travel ban.
A few tidbits about the row over Trump's selective ban on who can enter the US, and the related furore over his planned visit to the UK.