Lots Of Algae In My Cycling Tank

I am part way through my fishless cycle. The ammonia is being consumed nicely but my nitrites and nitrates are still off the scale. There is green hair algae on the walls of my tanks, and brown algae on my plants. I've got some small green lumps growing in the substrate, as well as some white specks. I can't work out what the white specks are - they don't look like worms or snails eggs, more like tiny bits of scale from a kettle.

What I have read suggests this is fairly normal, since the good conditions for bacteria in cycling are also good for algae. But it did happen very quickly - on Friday evening when I tested the water I saw a few brown spots on the plants and thought it might be algae. On Sunday evening there was no doubt at all, and the plants were not looking happy.

My plan is to give the sand a good vac, and do a major water change, this evening. I will try to wipe the plants down with a sponge. I've read brown algae is difficult to shift, and some people have thrown away plants as a result. That would not be a disaster, but I was hoping to establish the plants before I put any fish in. I suppose now might be a good time to use anti-algae chemicals, before I have any fish. But I am a bit cautious, since I don't know how they will impact the cycling.

I'd welcome any thoughts or suggestions - I'm an absolute beginner. I'm also interested how people deal with algae on plants in their mature tanks. I knew I was going to need to clean the tank itself, so bought a magnet, but I had not thought about algae on plants.

Thanks again Sue.

When I got home today there were 9" long stands of algae growing from the Vallisneria. That has been covered by brown algae, but is still growing so maybe it will survive. The Tiger Lillies won't by the looks of things, one already choked to death. A shame because they seemed to be doing really well until the weekend.

Anyway I cleared all the algae I could, rinsed the filter and did a 20% water change (I vacced up that much!). Fingers crossed!