I'm going to immediately qualify the title of this post and note that, in writing "Karma Police," Thom Yorke and the rest of Radiohead weren't necessarily inspired by The Beatles as much as they were drawn to borrow from them. Specifically, it's in the chord progression of the song's piano and acoustic guitar that you can hear The Beatles playing "Sexy Sadie," John's veiled rebuke of the Maharishi from side three of The White Album. The connection is pretty obvious. But whereas "Sexy Sadie" has a lighter feel to it, "Karma Police" is dark and uncertain, with an only somewhat restrained sense of menace at its core. It's an absorbing and perhaps perfect song, one of a half-dozen or so highlights from Radiohead's 1997 classic OK Computer.
And just because I've recently been writing about Smokey Robinson's heavy influence on John, I want to direct you to what Wikipedia has to say about some of the lyrics from "Sexy Sadie:" In a 1969 interview, Lennon stated one of his favourite songs was "I've Been Good To You" by Smokey Robinson & The Miracles. The Miracles song begins with the line Look what you've done / You made a fool out of someone, compared to Sexy Sadie's What have you done? / You made a fool of everyone.
We've now established a link, however indirect, between Smokey Robinson and Radiohead. Rad.