How can I prevent clothes and food stuff from going bad in a moist cabinet
I don't know what part of the world you're in, but I'm going to figure this might be mold, not algae.  Either way, a spray bottle filled with bleach solution will probably get rid of it.  Mix a gallon of water and a cup of bleach, and use that mix to fill the spray bottle.  Spray it on, wipe it, but don't rinse it off.  

Keep in mind bleach is harsh stuff, keep the place well ventilated, use care not to get it on yourself, or anything else besides the wall.  

edit:  the original poster commented that they were concerned about bleach ruining the paint.  This is a valid concern and a good reason to try this in a small and inconspicuous spot before doing the whole wall.  

I was curious and found this page 

http://www.howtoremoveblackmold.com/how-to-kill-black-mold.html

which had some other similar suggestions, along with bleach - ammonia, vinegar, borax, baking soda, hydrogen peroxide, and others.  If bleach turns out to harm the paint, maybe one of these would help.