Dozens of artists – including Pulp, Paul Weller and Primal Scream – have come out in support of the band Kneecap, as counter-terrorism police said they were investigating videos of them allegedly calling for the deaths of MPs and shouting “up Hamas, up Hezbollah”.

On Thursday, detectives said videos of the two incidents had been brought to their attention in late April, and had been referred for assessment by specialist counter-terrorism officers. They had “determined there are grounds for further investigation into potential offences linked to both videos”, officers said.

Scotland Yard added: “The investigation is now being carried out by officers from the Met’s counter-terrorism command.”

The Irish language group have been the focus of heavy criticism over the two video clips in recent days. Ministers have put pressure on the organisers of the Glastonbury festival over the group’s inclusion on the lineup, while a gig at the Eden Project has been cancelled.

The Conservative leader, Kemi Badenoch, has demanded the trio be banned from Glastonbury, with politicians from the governing and opposition parties highlighting the danger already faced by MPs after the murders of their colleagues Jo Cox and Sir David Amess.

The video footage appeared to show a member of the group saying at a 2023 gig: “The only good Tory is a dead Tory. Kill your local MP.” Footage from another date last year appeared to show one of the band shouting: “Up Hamas, up Hezbollah” – groups that are banned and defined as terrorist organisations in the UK.

However, in a joint statement also signed by other artists including the former BBC Radio 1 DJ Annie Mac and the bands Massive Attack and the Pogues, the group said there had been a “clear, concerted attempt to censor and ultimately deplatform” Kneecap.

“As artists, we feel the need to register our opposition to any political repression of artistic freedom,” they said.

“In a democracy, no political figures or political parties should have the right to dictate who does and does not play at music festivals or gigs that will be enjoyed by thousands of people.”

Massive Attack also put out their own statement, adding: “Language matters, of course. The hideous murders of elected politicians Jo Cox and David Amess means there’s no scope for flippancy or recklessness.”

It said politicians were “strategically concocting moral outrage over the stage utterings of a young punk band”, adding: “Kneecap are not the story. Gaza is the story. Genocide is the story. And the silence, acquiescence and support of those crimes against humanity by the elected British government is the real story.”

Kneecap have been outspoken on political issues, including British colonialism in Ireland and the Gaza war.

And they are not the first band to come under political and judicial pressure over their material. In 2015, the US rapper Tyler, the Creator was banned from the UK because of lyrics from a 2009 release. And, in the mid-1970s, many shops refused to stock records by the Sex Pistols over their content, while prosecutors unsuccessfully went after a record shop manager in Nottingham for displaying the band’s artwork – subjecting him to a trial under obscenity laws.

In response to the latest furore, Kneecap have sought to defend themselves; apologising to the families of Amess, the Conservative MP murdered in 2021, and Cox, the Labour MP killed in 2016. They said they “never intended to cause you hurt”, and that they “reject any suggestion that we would seek to incite violence against any MP or individual”.

The group said: “Kneecap’s message has always been – and remains – one of love, inclusion, and hope. This is why our music resonates across generations, countries, classes and cultures and has brought hundreds of thousands of people to our gigs. No smear campaign will change that.”

They added they had “never supported” Hamas or Hezbollah.

Families of both MPs have suggested the band’s apology was less genuine than they had hoped. Katie Amess, the daughter of the murdered MP for Southend West, said it would be “very dangerous” for Kneecap to perform at Glastonbury. Brendan Cox, the husband of Jo, called the statement “half an apology”.

He said: “It’s fine to say that you’re sorry for it, but the way that they have actually spoken about it is to suggest that it’s a conspiracy, that they have been targeted unfairly, and for me, that then doesn’t come across as unfortunately particularly genuine.”