Hi, and welcome to UK Fungi.
It looks like the remains of an old “puffball” type fungus – possibly one of the
Puffballs are common throughout the UK and release their spores either through an apical hole at the top of the mature fruitbody, or when something damages the outer “skin” of the fruitbody in some way.
The brown dust you mention would be a cloud of spores released when you moved/damaged the decaying dry fruitbody.
As a “one-off” type of occasion, I wouldn’t be too concerned over the possibility of having breathed some spores in. – There are spores floating about everywhere, and in our normal everyday lives we will all be breathing in several hundred spores (and a million and one other “invisible” microscopic things) during the course of a day.
Generally speaking, our respiratory system does a remarkable job in filtering out these everyday impurities before they can do us much harm.
Regards,
Mike.
