One of the toughest jobs in pressure washing is removing algae and slime from brick, as one false move with the pressure tip and you can dig a hole and ruin the brick. It is especially difficult to clean old buildings and walls, but it can be done and come out great if the right techniques are used. So, let me explain to you the methods recommended for this.
You see, for many years, I ran a company that franchised mobile cleaning units, and amongst other things we cleaned concrete, decks and brick work on homes. We did construction clean-up, restoration clean-up and general pressure washing spring cleaning for our many clients in many markets. Now then, the first thing you need to do is get a hold of a decent pressure washer, one which has a long wand and a 25 and 45 degree tip.
First thing you need to do is to rinse off the brick and get down past the basic crud to what you really need to be concentrating on; for this use the 45 degree tip and keep the nozzle a good 8-12 inches from the surface; start at the top and work down. Now you can better see what you are dealing with. So, apply some soapy water, with a little Clorox but not too much, and apply it with a semi-hard bristle brush lightly from top to bottom.
Next, take your 25 degree tip keeping it one-foot from the surface, starting from the bottom to the top carefully moving the wand back and forth. Once completed, see where you are at and repeat this process, soon the brick will be clean without digging holes or ruining it.