Hi Jonno
What is the sheet material on your ceiling. It sounds like it might be a hardboard sheet, like masonite, if it is a brown colour. Or do you mean the paper colour as in plasterboard sheeting? Either way you will need to remove all the peeling/flaking paint as even the best primer can't stick peeling paint to the ceiling. I would scrape all loose paint from the surface then sand the entire ceiling. One good coat of a sealer primer and two coats of a good quality ceiling white or perhaps a low sheen finish if this is a high moisture area.
Cheers
Bob W