Xbox writes: "We’re aware that some of you are unable to sign in to Xbox Live, but we’d like to assure you that we’re doing all that we can to straighten things out. Your patience is appreciated during this process, Xbox members! Feel free to check back in half an hour for an update."
"UPDATE 3: Microsoft has confirmed that the issue has been fixed as of 19:26 BST, and we can at least confirm it on our end. Let us know if you're still having trouble, but otherwise, happy gaming folks!"