Hi David,
As you do not have any census information to go by due to your grandmother being born after the 1901 census, certificates will be the only way for you to confirm the birth of your grandmother and her parents names.
I suspect that this is your grandmothers birth entry:
Births Sep 1903, Kelsey Lily Blean 2a 1004
From this information, you can order a birth certificate to confirm parental information.
_________________
From the fathers information you sent, I would suspect that that information is incorrect. I found a marriage entry for George Kelsey in the same location as Lily's birth:
Free BMD:
Marriages Mar 1893, Kelsey George Blean 2a 1047
Marriages Mar 1893, Stroud Caroline Maria Blean 2a 1047
Kent Registration Services:
Name: KELSEY, George, ,
Year of Marriage: 1893
Entry Number: 37
Register: BL/8
Location: CANTERBURY AND SWALE
Name: STROUD, Caroline, M,
Year of Marriage: 1893
Entry Number: 37
Register: BL/8
Location: CANTERBURY AND SWALE
____________________________
If you purchase the certificate for Lily and find that the above people are her parents, you can then start searching the census information for other family members.
I hope that helps.
Nancy