Buddysmum,
I recently purchased the death record for one of my ancestors and was saddened to learn that she had died in the Chatham Union Workhouse. I wondered if her family had been there, too.
I wrote to the Medway Archives and, for a small fee, they sent me a copy of her entries in the Admissions and Discharge Book from the workhouse. It showed me that only she was admitted, just eight days before she died of tuberculosis, so I know that she went there to die in the hospital.
They probably have the entries for your great-grandmother, as well. However, that won't tell you where she was buried.
Do you know what her religion was? You said she was living with her son before she entered the workhouse. Where was the son living? Do you have her exact date of death?
P.S. City Ark has a project called, "The Way of Death". They have started scanning and uploading images of more recent burial registers. Hopefully, they will have the Chatham area done soon enough, so you can go through the images yourself for free.
The most recent update says, "Plans to film and scan the Medway Council municipal cemetery registers (Gillingham Grange Road, Gillingham Woodlands Road, Strood St. Nicholas, Rochester St. Nicholas and Chatham Maidstone Road) in collaboration with Kent Family History Society (KFHS) and Medway Council Bereavement Services Section are in hand."
I personally can't wait because a lot of my folks will be listed!
Regards,
Josephine