Sir Tim, who was invited to edit the flagship news programme on Boxing Day, had intended to employ an atheist to read the traditional Thought for the Day, in order to best represent Britain as a whole.
But, he has disclosed, the move was prohibited by the BBC, which insists the slot must be filled by a religious leader.
When interviewed on the Today programme about the task of guest editor, Sir Tim said it had taken him “a little while to figure out what you can do”.
Speaking of his initial plans to have Thought for the Day delivered by an atheist, he said: “Thought for the Day was an interesting point. There I was saying if we have a thought, why can’t it be a thought from an atheist?"