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To clean algae from bricks, try a pressure washer. A typical D.I.Y. pressure washer usually won’t blast away mortar unless it’s already crumbling. They also have fine streams, so if you are concerned about the mortar, you could take the time to target just the bricks while avoiding the mortar as much as possible.
If you'd rather not risk it, you could consider hiring a professional who specialises in soft washing with chemical treatments. Any outdoor cleaning specialist should be able to assess the condition of the mortar and recommend the safest approach.
Another option is to periodically spray the area with 30 Seconds 5L Roof Treatment Concentrate. While designed for roofs, it can also be used on brick walls. This type of treatment works by killing the growth, which then breaks down and washes away over time. If your wall has a heavy buildup of algae, this process could take a while.
If you’re keen to handle it yourself, I’d suggest picking up a pressure washer and testing a small section first to see how the mortar holds up. Otherwise, a professional can ensure a thorough clean without causing damage. - MitchellMc
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