You'll not be able to completely get rid of the fungal infection... even the one on your lawn (sorry)... The toadstools are caused by organic material under the surface of the lawn... perhaps an old tree stump or some such. The "ring" you're observing is commonly called (at least here in the U.S.) a fairy ring, but also caused by organic material under the surface. There are chemical treatments that one can use with greater or lesser results, but, generally, by the time you go to the trouble, the infestation will be over for the season.
You can dig up the lawn and try to eradicate the primary cause, but that's a losing battle as well, in my opinion...
You could aerate the area thoroughly (core aeration by machine), fertilize often with a high nitrogen content fertilizer, and water the area only in the cool morning hours to help .... but it won't cure it.
Best of luck!