The singer insists he does not want the group's songs to be associated with the Conservative leader and has issued a stark warning to Cameron not to consider a Radiohead soundtrack when he starts his crusade to win a second term in office.
Yorke tells Dazed & Confused magazine, "I can't say I love the idea of a banker liking our music, or David Cameron. I can't believe he'd like (Radiohead's last album) King of Limbs much. But I also equally think, who cares?
"As long as he doesn't use it for his election campaigns, I don't care. I'd sue the living s**t out of him if he did."
British rockers Keane previously criticised Cameron for using the band's hit Everybody's Changing as his political anthem in the run-up to the U.K.'s last election in 2010.
Frontman Richard Hughes wrote on Twitter.com at the time, "The Tories (Conservatives) played Keane at their manifesto launch (sic). Am horrified. To be clear - we were not asked. I will not vote for them."
In America, Survivor rocker Frankie Sullivan sued Republican presidential hopeful Newt Gingrich for using the band's hit Eye Of The Tiger during his campaign, while Twisted Sister star Dee Snider ordered Mitt Romney's vice presidential running mate Paul Ryan to stop using the band's song We're Not Gonna Take It.