You probably just need some more plants. I know it is difficult with the Goldfish, but people can probably advise you of larger leaved plants that they don't eat. The algae is Black Brush Algae (BBA), we don't really know what causes it.Anybody?
Plants need all of the nutrients required for growth, one of the "big three" is phosphorus (P), it is a huge issue in <"natural wetlands">, but I honestly don't think it is your problem. Marcel @zozo has Goldfish in his outside "tanks", I'll add him in.I DO have phosphates in my tap water, so must have done the test incorrectly last time! Assume this contributes to the algae? How can I reduce levels?