Dust like powder on walls

Try some solvent base undercoat on it. It is damp which is coming though causing the problem but undercoat should hold it

i would not treat it with anything until you have found out were the problem is coming from, you will only be covering up what will never be cured. get it sorted by a builder and then let it dry out, followed by treatment given by your builder.

Yes I agree with D.J Decorators, in order to stop it you have to find out where the water is coming from. Often sorting out damp isn't as scary or costly as you think, as it could just be one little hole or bad piece of guttering somewhere that just requires repair and the problems solved.

In addition to the answer ... need to see it , but to me it looks more like Efflorescence on the walls. One of the ways to remove it is by using household diluted white vinegar. It’s less harmful than industrial chemicals , which is good. And after the treatment can be used undercoat and paint. Hope the information is helpful... Kind regards Anna

Sounds like efflorescence, best way is to brush it all down with stiff brush, wash it with something acidic- like a vinegar not malt wait for it to dry and wipe it down with a damp cloth and let it dry. Use some oil based emulsion to cover area and then cover with top coats of colour of choice to finish off. It’s quite harmless