It's down to the written orders of the Prime Minister, isn't it? Some previous PMs have said they wrote orders saying no strike, IIRC, but what do we think BoJo would do? I'm guessing nuke-all-the-things. Possibly first having scrawled Chhhuuuurrrrcchiiillllllll!!!! down the side of the nuke in crayon.
If they have autonomy to strike in a last resort situation not sure what is in the letter will matter much.