Internet sites can be useful, but generally you make more progress doing it the old-fashioned slow way.
So for instance, actually pay to get hold of your great-grandmother's death certificate, if you haven't done so already. This might give you info such as where and when born, possibly details of her husband, details of who the informant was - often a spouse or child.
If you know roughly when she married, get hold of the marriage certificate and you might get some more clues from that - name of her father and her father in law for example.
If you know her birth date, or even the rough year, search the indexes to get her birth certificate, that should tell you her mother's name and hopefully the father's too.
Use the census material - a lot of it is available online on a pay-per-view basis, such as the 1901 census, or you can visit libraries or local record centres if you happen to live in the right area.
If you painstakingly get the birth, marriage and death certificates for each person you're interested in, and hopefully find some census data, this gives you lots of info and helps you slowly move backwards a generation at a time.
Have a look on www.freebmd.org.uk - this has lots of indexes to births, marriages and deaths. It's not complete yet and not totally infallible, but it's free and a very useful too. I always start there.