Most people will say try some antibiotic tablets.
Instead I tried a complete blackout of the tank for three full days, no feeding, no peeking.
Worked a treat. I was almost blinded with how light the tank looked after weeks on end of dark algae. As soon as I'd uncovered the tank I took all the water, plants and substrate out (inert silica sand) and replaced with a nutrient rich substrate (soil) with a layer of sand on top and replanted.
Since then I have no sign of the BGA. A lot of brown diatoms as the water was all new though, but I hope this will clear.
The point is that a blackout may well work but unless you get to the root (haha) of the problem and sort it out, the algae will probably return at some point soon. Make sure you have plenty of fast growing stems to use up nitrates and phosporus.
Hope this helps