Hi and welcome to Roots
Have you tried to find a death certificate for the baby?
I'm not sure on the Leeds area, but I know in Middlesbrough, when babies were stillborn, they were quite often buried in a grave with a adult. The baby would just be placed within the coffin. It was high lighted a few years ago and now nearly all the babies graves have been marked in some way.
I would imagine the best way to find out would be find the local cemetery/graveyard and ask in the office, or contact the council for the area, under bereavement services.
Good luck
Jane