Posted: 06/12/2015 at 09:23
Can't see them well enough to attempt an ID, but I wouldn't worry. Most gardens have fungi of one sort or another appearing in mild damp spells, especially in the autumn. They're part of nature's way of breaking down organic matter in the soil so that plants can make use of it. The ones in your lawn may well be breaking down the roots left in the ground after your tree was felled.
The toadstools that you see are simply the fruiting body - the main part of the fungus is the mycelium underground which can spread over vast areas.
Some may be toxic to some degree, some may not. Most animals leave them alone, but if you have the sort of dog that just has to try to eat everything then you can sweep up the fungi and bin them.
Improving the drainage in the lawn may help to reduce the number of fungi you get in the future.
I hope that helps