The general rule of thumb is that British citizenship can only be transmitted down one generation outside the UK. Furthermore, before 1983, it was only transmitted down the father's side. So, given the fact that it was your great grand
mother, things are already looking weak.
But the history of British citizenship is very complex with multiple changes over time. To address your query, we would need a more complete picture of your whole family (details of your relevant parents' birth places and month/year, likewise for your grandparents').
Also have a read and look through the further reading list in
a thread with a similar question.
People who have at least one grandparent born in what is now the UK (including the whole of Ireland before 1922) can apply for an Ancestry visa, not direct citizenship. After five years of residing and working in the UK under the Ancestry visa, the person can then apply for ILR, followed a year later by British citizenship.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.