Pepsi has said it is withdrawing its sponsorship of a UK music festival that is due to be headlined by Kanye West after Keir Starmer joined criticism of the event.

The musician is understood to have not yet made an application to come to Britain and could be blocked under powers allowing the authorities to do so if his presence is deemed not conducive to the public good.

The prime minister joins others who have criticised Wireless festival for booking the musician, also known as Ye, to headline all three nights of the forthcoming event in London.

The rapper has drawn widespread condemnation in recent years after he began voicing admiration for Adolf Hitler, and has made a series of antisemitic remarks.

Last year, he released a song called Heil Hitler, a few months after advertising a swastika T-shirt for sale on his website.

However, there are now serious doubts about whether the festival, which is due to take place in London’s Finsbury Park in July, will go ahead. A Pepsi spokesperson said: “Pepsi has decided to withdraw its sponsorship of Wireless festival.”

Starmer said: “It is deeply concerning that Kanye West has been booked to perform at Wireless despite his previous antisemitic remarks and celebration of Nazism.

“Antisemitism in any form is abhorrent and must be confronted clearly and firmly wherever it appears. Everyone has a responsibility to ensure Britain is a place where Jewish people feel safe and secure,” he added, in comments first reported by the Sun on Sunday.

Ed Davey, the Liberal Democrat leader, has called on the government to ban West from entering the UK, saying: “We need to get tougher on antisemitism.” He described West’s planned appearance as “extremely serious”.

The home secretary, Shabana Mahmood, could personally direct that West be excluded from the UK.

While the Home Office does not comment on individual cases, recent ones have appeared to include Eva Vlaardingerbroek, a Dutch anti-immigration influencer who has promoted conspiracy theories such as the “great replacement” and who said she had her authorisation for visa-free travel to the UK revoked earlier this year.

UK immigration rules state that a person can be denied entry based based on their character, conduct, or associations when these pose a threat to UK society. This applies to conduct both in the UK and abroad.

The test is applied on a case-by-case basis, while Home Office guidelines list scenarios such as if the person has engaged in extremism or other unacceptable behaviour. The latter includes views that “foster hatred which might lead to inter-community violence in the UK”.

The Jewish Leadership Council last week condemned Wireless festival for booking the rapper, who will appear after heightened attacks on the UK Jewish community. The conduct of the organisers was “deeply irresponsible”, it said.

Phil Rosenberg, president of the Board of Deputies of British Jews, has also said it was “absolutely the wrong decision” to allow West to play.

West apologised in January for his antisemitic remarks in a letter published as a full-page advert in the Wall Street Journal.

In his letter, he apologised to Jewish and black people, and said his bipolar disorder had led him to fall into “a four-month long, manic episode of psychotic, paranoid and impulsive behaviour that destroyed my life”.

Wireless festival, which is sponsored by Pepsi, has been contacted for comment.