The reason for asking is that shaggy inkcaps have come out in the second week of august for the last two years. Today I have found one starting to grow.
You need to remember that the fungus we see - the mushroom or toadstool - is only part of the whole organism. It is the fruiting body, like the apple on an apple tree. Most of the fungus is a thread-like structure in the substrate - underground, in the wood of a tree, the inside of a potato, or in some cases within an animal.
It's a long time since I did any mycology, but two things appear to be required for a fungus to fruit.
First, it needs enough energy to do so - feeding off the host or the dead material it is growing in for a while to have enough energy to spare to produce the fruiting body and develop it.
Secondly, it needs conditions that are best suited to the dispersal of the spores. So it needs to be able to sense the ambient conditions, and I'm not sure if it is well understood how this happens.
Take a stinkhorn as an example. It relies on flies to disperse the spores. So there is no use it fruiting when there are no flies on the wing - say in the depths of winter.
Certain species can and do grow almost through the entire year, as with this species, while others are much more dependent on the season and weather.
All given ID's are subject to error/ommissions. Please seek independent verification before acting on ANY advice given. BE SAFE =)