There are 2 things algae need to survive: food and light. Cut out either one and you'll have an easier time getting rid of the algae.
Since you don't have a protein skimmer to remove excess nutrients in the water column, you may have to resort to cutting off the lights. It appears that the only photosynthetic creature you have in the tank are the anemones, but they should be fine if you don't over due it with the darkness.
Once upon a time, I had to deal with hair algae in my reef tank, which was annoying and hard to get rid of, so I tried the 'darkness' method. In a tank your size it may be a bit of an undertaking, but it can be done.
First, cut off all (and I mean ALL) sources of light, specially natural sources (like sunlight coming in from a window or doorway)...the easiest way to do this is by wrapping up the tank with black garbage bags (that's what I did) and turn all the lights off. Leave your filters and pumps running, as a matter of fact, try to increase circulation to help dislodge and remove the dying algae. Having sensitive corals in my tank, I only kept the lights off for 3 days and it worked well. There was massive algae die off... which means additional pollution in your tank. As soon as you're done with the darkness process, you MUST do a major water change to further remove the die-off.
I would also recommend that you minimize your feedings as much as possible, get algae consuming creatures (Snails, urchins, sea hares and certain blennies do this very well - do some online research), and last but not least, reduce or eliminate phosphates in your tank! I would recommend getting a phoban reactor, very cheap -$30 bucks- and you'll need a small pump and phos-ban media (easily found at any marine aquarium store), and you'll be doing yourself a big favor in means of algae reduction.
Hope this helps...