Every burial should be recorded by whoever is responsible for the cemetery, including the location of the grave. In the past, however, it was the practice not to treat stillbirths as 'proper' burials, and as you say there may be more than one baby buried in the same plot. Many authorities also forbade the erection of headstones, though some would allow a small plaque. All of this can make finding the exact spot difficult. Even so, I would expect there to be a record of the area where stillborn babies were buried.
The funeral director may be able to help, especialy if the firm is still in the same hands (many now belong to large companies), but in many cases their duties ended when they delivered the coffin to the cemetery. You say that it is a 'public' cemetery, so I would be inclined to write to the head of the appropriate department of the local authority - their website should have details.
You may also find
SANDS Stillbirth and Neonatal Death Society useful.