Hi Cath. Certainly looks like Ganoderma. They are notoriously difficult for the amateur to separate.
You are spot on with what you say about the environmental conditions. Soil compaction, fertiliser use, excessive nitrates from animal dung and changes in hydrology, that kind of thing, can all tip a tree over the edge and increase the susceptibility to fungi and the impact that they have on tree health. It is quite normal for a tree of this age to have a range of fungi living in/on it. Limiting trampling, around the roots (perhaps with a fence), consider reducing stocking density and timings (in wet weather the ground will obviously get more poached) and consider applying a wood chip mulch around the base of the tree, which will help to aerate the soil by stimulating biological activity. I think it's worth bringing in a consultant for advice and to draw up a management plan to ensure the best for your trees.