You don't put the spawn in the soil at all. You follow the instructions, and grow them on "a 2 square metre bed of waste cardboard and woodchip" - http://gardengiantmushrooms.co.uk/the-garden-giant-mushroom/
It is true that good soil contains many species of fungi which are symbiotic with plants, but the suppliers don't seem to be making any claims about this species (Stropharia Rugosoannulata) - and in any case, it is not a native British species.
Most of the mycorrhizal fungi which are symbiotic with food plants actually live partially inside the plant roots and don't produce edible fruiting bodies above ground. The ones that do generate edible "fungi" (including Stropharia Rugosoannulata) are mainly associated with woodland trees like pines, firs, and oaks. (Lots of pictures here - http://www.alansblog.org.uk/?p=4165. That's why you grow it on wood chips and cardboard - so far as a fungus is concerned, cardboard is just more decomposed wood.
So if you want to try the fungi, and/or have an interesting talking point in your garden, by all means grow Garden Giant - but don't expect it to do much for your other food plants IMO.