Not sure which fungus it is, hopefully not honey fungus, but you can't get rid of it now it's there - its likely in association with the dead roots under the soil. These toadstools are only the fruiting bodies of underground mycelium, the sort of 'roots' of the fungus, and they will appear every year and may spread. If you removed all the dead wood, the patch might not get larger.

Thank you Bamboo. I might dig down at the end of season and investigate what is there.

It looks like one of the many forms of puffball. If so, it is probably harmless. The best way of dealing with it that I can think of is to apply 48 hour compost tea a couple times a year, to increase the diversity of your soil flora. That will increase the competition for those roots, and prevent masses of puffballs, though you might still get a few.

Why bother? This type do no harm and will disappear very soon in any case.

True, Owdboggy! But it's the same reassurance that I give customers that come in with slime mold sporing structures, and it's not often listened to.

Thank you all.

They are earthballs and harmless. The little holes in the top are where the spores have been ejected. They mostly occur on bare soil so its no use digging down for anything they are growing from. Just leave them, they are quite fun really. You may see them again next autumn.