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Radical preachers, segregationists and terrorist sympathizers have been barred from Britain in recent years, but should Donald J. Trump, the American billionaire and front-runner for the Republican presidential nomination, be given the same treatment?

That is the question to be discussed on Monday by the Petitions Committee of the House of Commons, where lawmakers are obliged to debate the issue after more than 573,000 Britons signed an online petition this fall. It says that Mr. Trump’s proposal to bar Muslim immigrants from entering the United States amounts to “hate speech.”

There will be no vote on the matter, and, in fact, the lawmakers do not have the power to bar Mr. Trump – that belongs to the British home secretary, Theresa May. But the debate underlines the extent to which Mr. Trump’s campaign has polarized opinion beyond the United States and provided some Europeans with a new American stage villain.

After the shootings in San Bernardino, Calif., last month, Mr. Trump urged a “total and complete shutdown of Muslims entering the United States until our country’s representatives can figure out what is going on.” He has also claimed there were places in London and other cities in Europe “that are so radicalized that police are afraid for their own lives.”

Prime Minister David Cameron has described Mr. Trump’s comments as “divisive, unhelpful and quite simply wrong,” but his government has said that the powers to exclude non-European citizens “are very serious and are not used lightly.”

Mr. Trump appears to have taken the threat seriously enough that his company, the Trump Organization, said in a statement that it would pull back from plans to invest more than $1 billion in Scotland should he be barred.

Alex Salmond, a member of Parliament from Scotland and former leader of the Scottish National Party, said on Sunday that barring Mr. Trump “would do him some good.”

The leader of the opposition Labour Party, Jeremy Corbyn, said he would not bar Mr. Trump, even though it appeared that Mr. Trump has “a problem” with Mexicans and Muslims. Instead, Mr. Corbyn invited him to visit his London constituency.

“As you know, my wife is Mexican and my constituency is very, very multicultural, so what I was going to do was go down to the mosque with him and let him talk to people there,” Mr. Corbyn told the BBC.