The actor’s next film is The Power Of The Dog, scored by Greenwood, where he plays cowboy Phil Burbank who runs a ranch in Montana with his brother George (Jesse Plemons).
“[Radiohead producer] Nigel Godrich and Edgar Wright came to see me in Hamlet,” Cumberbatch said. “They came backstage afterwards and we had a nice, long chat.
“I said to Nigel: ‘I’m a massive Radiohead fan, I don’t suppose any of the boys would want to come and see some Shakespeare?’ So Jonny and Thom came one night and afterwards we talked backstage.
“I was really nervous because it hadn’t been a great performance, so I was looking at the ground all embarrassed. But so were they – and Thom was muttering: ‘Yeah, we’re really big Sherlock fans…’ There was all this shifting around, all looking at our shoelaces. It was so weird!”
With his passion for music, however, would the actor ever star in a musical biopic in the vein of Rocketman or Bohemian Rhapsody?
“There are some rock stars I’d like to play,” Cumberbatch said. “But I don’t think it’ll happen and I’m not going to say who. You’ll have to guess.”
Asked about Radiohead specifically, the actor replied: “Oh I don’t think they want their lives made into a film. It would be quite a weird film, love them as I do. No not at the moment, but you know, we’ll see. Watch this space.”
Cumberbatch has a busy schedule ahead, starring in biopic The Electrical Life Of Louis Wain and two Marvel projects in Spider-Man: No Way Home and Doctor Strange In The Multiverse Of Madness.
The Power Of The Dog will be released on Netflix from December 1.