Gary I have fairy rings in my garden, and a fungus grew like a white plastic across the surface depriving the grass of water and subsequently killing it. It got so bad that we contacted a grass maintenance company who came in and aerated the lawn and applied a fungicide and a wetting agent. This has helped but the company told us that this will only push it back and not kill it. I am keeping these areas aerated and wet but the toadstools do still keep coming. You can not buy the fungicide they use it's only for industrial use 
Apparently the only way to get rid is to literally dig it up, I read somewhere 2 feet deep and 2 foot either side of the ring and dispose of the soil but when they are as large as the ones in my garden this is not realistically possible.
My lawn is a lot better at the moment (called the company in March) but I'm going to have to keep a close eye on it.