Michael,
First thing to figure is where the problem comes from. You have four options:
1). A leak in pipework (obvious,but always worth starting with)- probably not your problem tho,
2). Airborne humidity - from cooking, respiration, washing- hot moist air hits cold surface (tenement wall) and condenses. Minerals in plaster + water=food for mould bacteria. Bathrooms and kitchens are a no-brainer here. Does the kitchen have an extract fan? Could be worth fitting. Does the problem affect other rooms on this wall? A give-away sign- do the windows steam up? Double glazed units are normally pretty well sealed, but if they steam up, being the coldest surface in the room, generally, you have a condensation problem to deal with. This is sometimes less obvious with the old sash-and-case single glazing, for although they are colder still, they can be draughty enough to prevent condensation forming. Often condensation problems on walls affect areas higher up than you suggest, and in corners.
3). Rain Penetration from outside- how thick are the walls? Assuming it's a tenement, they are mostly rather badly built, and they depend on the wall thickness to avoid moisture penetration. Behind the thin veneer of dressed external stone the wall mostly is a random rubble that you can crumble by hand often

. The actual crapness of this, it being full of voids, helps to prevent water getting through. Built- in cupboards, where the wall is thinner, are cuplrits though. Worth checking if there are any features outside around the affected area such as stone projections-string courses, cornices etc that could be gathering water on the top-side and channeling it through the joints. If the building is rendered this helps, and yeah, some of the exterior sealants are now pretty reasonable, but have a limited life-span.
4). From the ground. The likely suspect in a ground floor flat. How old is the property? Does it have decent, unbridged damp-proof courses? How far off of the ground is the internal floor? Is there a void below floor?
Need to know more to answer, but don't start stripping walls until you know what needs done...if the guy is just guessing you will have repeat problem soon enough.
Temporary solution is to treat the wall surface as you suggest, but few treatments kill all the bacteria, or penetrate far enough into the substrate, and are obviously not addressing the cause. Do a google to get an idea of the best washes- some are useless.
If you are gonna hang onto the place for more than a couple of years it is worth fixing- mostly the bits you can see are the tip of the iceberg, and usually cost more the longer they're ignored IMHO.
Oh, the other possibility is that your tennant relieves himself on the walls

Actually came across this once!
Any strange customs in Poland?
HTH