I have first hand experience of this. The moisture causing the efflorescence is quite likely coming from the room itself. The structure becomes salt-poisoned through reactions of combustion products with building materials. The salts are hygroscopic, and when wet trades are applied easily migrate to the surface while the plaster or whatever dries. On the surface they continually pull moisture from the air and grow crystals.
I have had pretty good success around my fireplace by stripping to bare plaster then painting first with a dampseal paint (ronseal dampseal) - not to keep the moisture in, but to stop room moisture getting at the salts. In hindsight, I would have tanked the bare bricks with SBR slurry before plastering.
Going back a few years also originally had uncowled chimneys and agree this is a source of wet chimneys.