Much easier said than done even with chemical control!
You could try a solution of 20z of Epson salts in a gallon of water, spike the affected area and apply with a watering can.
If this does'nt work try 1/2 0z of sulphate of iron in a gallon of water per square yard.
If no joy with that, then its a case of removing the turf from the affected area ,plus a bit more and several inches of soil. Replace with fresh/clean top soil and either re-seed or re -turf Good Luck Tbird+
I had Lichen in my lawn which is a type of fungus, and was able to erradicate it ( after trying several products ) with a treatment called Armillatox - it is listed as a patio cleaner and as I said gets rid of Lichen, Moss and Algae.
Worth a try ?
Ta woodchopper I've been to all the local garden places looking for said armilotox but no-one's heard of it ,,someone else told me about it a while ago but i can't get my hands on it :-( local garden centre told me to spread Lime on it so I've done this today ..can only try