efflorescense is wat its called, it is salts from the bricks/mortor due to bad weather it runs down the wall try brick acid

The problem could be a number of things really. The best thing to do is, when its dry, clean the brickwork and apply 2-3 coats of brick & mortar sealer. You can get this at any large DIY store.

when laying engineering brick, the morter does not need to be so wet, as they are non as porous as normal house bricks, try using linseed oil with a rag and wipe on bricks, this makes the bricks shine and you lose the whiteness in the staining of the mortar. it could be efflorescence (salt) thats coming through but clean again, maybe with wire brush and rag linseed on the brick, taking care not to get it on the mortar.

use linseed oil not brick acid takes the colour out the brick