The US rapper, who has been condemned for anti-Semitism, is set to top the bill for all three nights of the festival in London's Finsbury Park in July.
Pepsi and Diageo withdrew their sponsorship of the festival after West was announced as the headline act.
The musician, who has not performed in the UK since he headlined Glastonbury in 2015, has drawn widespread criticism in recent years after he began voicing admiration for Adolf Hitler, and has made a series of anti-Semitic remarks.
He released a song called Heil Hitler in 2025, a few months after advertising a swastika T-shirt for sale on his website.
West, also known as Ye, has been barred from X over anti-Semitism on multiple occasions.
Prime Minister Keir Starmer joined criticism of the music festival at the weekend, saying it was "deeply concerning" that West had been booked to perform "despite his previous anti-Semitic remarks and celebration of Nazism".
In a post on X, the Campaign Against Antisemitism said: "The Prime Minister is right to be deeply concerned that Wireless Festival wants to headline someone whose anti-Jewish bigotry has gone as far as recording a track titled 'Heil Hitler' less than a year ago.
"But the Prime Minister is not a bystander.
"The Government can ban anyone from entering the UK who is not a citizen and whose presence would 'not be conducive to the public good'.
"Surely this is a clear case."
Labour MP Rachael Maskell said West should be banned from entering the UK over his previous anti-Semitic comments.
"We cannot allow these performers to have a platform, and that's why it's absolutely right that the prime minister has said that that festival, the Wireless festival, should cancel that performer," the MP told BBC Radio.
"But also he should not be allowed to come to our country to perform in the light of the anti-Semitic comments that he has made and recorded."
Jewish community organisations have criticised the festival, with Phil Rosenberg, president of the Board of Deputies of British Jews, calling on the government to consider barring him from entering the country.
In January, West took out a full-page advertisement in the Wall Street Journal to apologise for his anti-Semitic comments, saying his bipolar disorder caused "a four-month-long, manic episode of psychotic, paranoid and impulsive behaviour that destroyed my life".
Wireless Festival has been contacted for comment.
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