Are those chalky deposits from the paint/coating above?
Do you ask for the efflorescence white sh*t remover?I've read a ton of threads on the Powerwash board concerning that very thing. It's efflorescence and the product you want us available from your local brick supplier.
That picture, or one like it, is posted about once a week on the couple of power washing boards I frequent.
There's two or three different products they always mention, but I've learned by lurking that those products are found at local brick suppliers, and the correct one is whatever they happen to carry.
Soda would not only take it off but make all of that brick look like new.soda blast??