Ms. Hopkins, a former Sun and Daily Mail columnist who appeared on the British version of “The Apprentice,” has become well known in Britain for her provocative views.

In a 2015 column, she compared migrants to cockroaches. And after a suicide bombing killed 22 people at an Ariana Grande concert in Manchester in 2017, Ms. Hopkins tweeted that “we need a final solution” to the terrorism problem. She later deleted the post.

Sowing fear of Muslims — and calling out other politicians for not using the phrase “radical Islamic terrorism” — was a bedrock of Mr. Trump’s run to the presidency in 2016. In an interview that March, he told the CNN anchor Anderson Cooper that “Islam hates us.” The previous year, he would not rule out a mandatory registry of Muslims in the United States in an interview with Yahoo News and, after a mass shooting in San Bernardino, Calif., called for a ban on Muslims entering the country.

Ms. Hopkins’s tweets and commentary were first a source of affirmation for Mr. Trump in his campaign.