Based on experience in my own house, it's salts in the wall. Victorian houses which had lots of coal fires will have salts in them all caused by combustion products reacting with, in particular, lime based materials. I still have a little battle going on with salts around the side walls in my fireplace - I know the only ultimate remedy is to chop out all the salt laden bricks and rebuild. Interestingly, when we were doing the refurb we also had some salt patches showing up where the dabs were on some newly boarded walls - the wet in the dabs drew the salts through the PB. However these did disappear once we got heating on.
Based on my own experience, I would strip the wall and re-board using a foam board adhesive rather than a wet board adhesive to secure the boards. The foam will insulate the boards from the salt-laden bricks.