Ms Hughes killed Mr Green!
Mrs. Hughes was at the Abbey, helping to set up for the Church bazaar, on the day Mr. Green was killed.
I can't see kind, comforting Mrs. Hughes murdering someone, no matter how angry she was at him and despite the fact that she threatened him!
Of all the theories I've heard, the Edna Braithwaite theory sounds best, or another one of Green's victims (if not one of their relatives).
My guess is Lady Mary. She made a flip comment/joke in the finale about being left alone with Edith after Tom leaves and she would kill her and go to jail for her murder. Foreshadowing. Also - I think that they may have arrested Anna as a ploy to get Lady Mary to confess. And Lady Mary said that she "knows" Anna is innocent. Anyway, I say they allude to it at the end of the Christmas Special and leave us all waiting...