I am under the impression that stillbirths are simply buried in any convenient open grave, and don't have a grave of their own?
Not quite, all burials have to be registered (from 1864) and the burial of the still born would be recorded in the burial register.
See the Registration of Burials Act, 1864
http://www.rootschat.com/links/01nmu/Even before that date, from at least 1551, the burials of many stillborns have been recorded in burial registers and many buried in the church itself.
Cheers
Guy