Hi,
Based on the assumption that your stepgrandfather formally adopted your mother, after your grandmother's relationship with your biological grandfather ended, you could begin by obtaining your mother's birth record from the General Register Office (GRO). In order to find this, you may need to search the GRO Index using your mother's first name and your biological grandfather's surname. If you can not find a relevant record, then it can be assumed that your biological grandfather is not on your mother's birth certificate. If you do find a relevant record, then the certificate should include some information about your biological grandfather, e.g., his occupation.
If your biological grandparents were married, then their marriage certificate should also provide his occupation, as well as the name of his father and his father's occupation.
Once you have collected enough relevant names, locations, and dates, you can begin to check census records and electoral rolls. After collecting this information, you will be better able to investigate relevant records further.
All the best,
