Get rid of the damp first. Until then, mould will come back, and paint will not stick. It will stop growing, and die, when the wall is dry.
Pull off all the wallpaper around the damp, you can wipe it with a bleach solution (it will smear) which will kill it for a while, as will the more expensive sprays.
Don't waste your time trying to redecorate until it is dry.
In a high corner of an upstairs room it might be caused by a gutter defect. You may be able to see if you borrow some binoculars. Also look during and after rain as it may drip for a while. If you're really lucky it will be caused a leaf blockage, or it might need repair.
Have a look in the loft for any damp in case it is a leaking roof or pipe.
There are people who specialise in gutter cleaning and repairs, but get a recommendation from someone local (not an advertising website). It's quite common for plasterers to also do rendering, if they don't mind heights.
If the damp patch is all along the tops of external walls, it may be condensation. Post some photos please. There is a way to check.