My tank (10 gallon with 28 watts of lighting) was also run over by hair algae, because I don't have any CO2 system, and it is very densely planted. For the last week or so, I turned off the lights for 2 hours in the middle of the day every day, and now my hair algae grows much slower, and there's much less of it.
Turning off the lights in the middle of the day gives less light to the algae, and the algae is a low form of life, so it affects it adversely, but the plants can still photosynthesize a few hours after the lights go off. You should try to see if this works. It worked for me.
Also, hair algae can be caused by excess of phosphates. The hair algae started coming up after I overdosed with nutrients that contained a lot of phosphates.