The white stains described are probably either efflorescence or calcium carbonate. Efflorescence occurs when water dissolves salts in brick & mortar, bringing them to the surface & leaving them on the face of the wall, these stains can usually be removed with water & a brush.

Calcium-carbonate stains are also caused by water in the brick which dissolves calcium hydroxide in the mortar & when exposed to carbon dioxide in the air forms calcium carbonate. These stains are thick, hard, crusty, & are not water soluble. Muriatic acid must be used to remove these stains.

Water in the wall is the cause of each case & an initial outbreak is fairly common & not a serious problem. If either persists over time, however, it is an indication that water is entering the brickwork on a regular basis & corrective measures would need to be taken in order to identify & repair the point of entry.