How can I clean exterior pebble dashing?
I doubt brickwork would leach through the typical 1" or more of mortar.  It would have to be something near the surface.  

A mild detergent with a mildewcide added should be sprayed on, allowed to soak per directions and then scrubbed lightly, followed by a rinse.  If the red dye comes out, I would use a sealer to help the surface dry off more quickly after a rain and it will keep the walls cleaner.