Where might I find a report on the inquest into this death?

Inquest was held on the 4th October 1871 by F Carter(?) Coroner for the Forest division of the County of Gloucestershire.

It may be amongst these when they are transcribed and available on the site.

Forest of Dean Inquest 1868-1874 - New Project
http://www.forum.forest-of-dean.net/index.php?mode=thread&id=11297

Could also be included the Gloucester Inquests. Both the Forest of Dean and Gloucester Inquests records are held at the Gloucestershire Archives.
http://www.gloucestershire.gov.uk/index.cfm?articleid=1348