Tracing guardianship, where to start?

Question:

Tracing guardianship, where to start?

I'm starting out on finding my grandmother's ancestry.
Her parentage is a mystery as she grew up with a guardian and neither my grandmother nor her guardian ever spoke about how or why this was so.
My grandmother used her guardian's surname as hers before she married so we don't know her birth name.
My grandmother's maiden name was Bertha Gilleis Haslam, known as Gilleis (note the unusual spelling).
Her guardian was a Dr Kate Haslam, born around 1875 and died around 1958. She was an early psychotherapist and lived in London in the early years of the 20th century.
Does anyone know if there would be official records relating to the granting of guardianship and if so how we might go about tracing them?
Thanks for any help you can give a novice in this game!

Best Answer - Chosen by Asker: IF YOU FIND OUT WHERE THE Dr. worked then you may find records of patients that could have been fore-bearers.