Eight years ago we were faced with this very problem with a property we bought. We used a floor brush, one of those things designed with a removable sleeve/cover/glove to be wetted to wipe floors with. We used a standard floor detergent mix and went over the ceilings which were the worst. We went over these perhaps three or four times, on the last pass we basically saw no difference and left it at that. Some parts of walls got the same treatment. Not long ago people were asking us if we had painted everything when we took it over, no, the original paint is there still and looks that good. However, I would say that we were/are very impressed with the paint that has been used, an emulsion of some sort - we have used something similar elsewhere in that house where the walls were still "naked" (a utilities room). The significant point to mention is that this was not in the UK where I would not be surprised if the paint began to come off from the cleaning work - I very much doubt that such quality paint is in widespread use here. You can try over a limited area, at least you might then find you can save yourself the effort of other complicated remedies and/or priming. This was very easy indeed and, frankly, the result is a delight.