As you appear to be quite new to this, you should be aware that all of the above are only probabilities and need to be confirmed with Birth Marriage and Death certificates.
For information contained on England and Wales BMD certificates have a look at this site:
http://home.clara.net/dixons/Certificates/indexbd.htmAs you already know your grandmother's parents names are James Brown and Frances Coppock, your best starting place would be your grandmother's birth certificate which you can order online from the General Register Office (GRO)
https://www.gro.gov.uk/gro/content/certificates/default.aspusing the following information:
Births Jun (Quarter) 1898
BROWN Alice May
District: Chorlton
Vol: 8c
Page: 778
Before ordering it's always a good idea to check the reference on FreeBMD and also the scan of the page as transcription errors can sometime occur.
Then the next step would be to order the marriage certificate of Alice May's parents - James Brown and Frances Coppock. Which should give you their respective father's names and occupations.
If you need any more help with this, please feel free to ask.