The outspoken musician has warned the British Prime Minister not to use any of his tracks to promote himself or the Conservative party, but doesn't care if the politician is a fan.
He told 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.''
The 'Creep' rocker may have made his feelings clear, but he insists he hates writing about politics in his music.
Thom said: ''The 'David Kelly' thing [a 2006 song about the death of the titular weapons expert] was very much an exception.
''I thought it was just so horribly English, so f***ed up. [But] politics is not a fun thing to write about.''
The quartet - completed by producer Nigel Godrich and percussionist Mauro Refosco - will release debut album 'Amok' next month, but Thom has ruled out a Glastonbury appearance in the summer.
He explained: ''We won't have got our s**t together by then.''