Charlie Brooker was asked at some point and couldn’t do it, but he seems somewhat open to the idea:

" I was sort of asked about Doctor Who once. I wasn’t asked to run it, I was asked to write for it, and it felt a bit like the Home Office asking you to do something – like it was my national duty…"

“But I just didn’t have time because I was busy.”

“So, if a big behemoth like Star Trek asked me to write for them, you’d at least take that call, wouldn’t you? You’d consider it. But with doing Black Mirror, you’ve got control; and when you wander into somebody else’s show, you’re trying to please them.”