Genealogy Questions? Ask a Genealogist for Answers ASAP
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Do you have a copy of his original birth certificate (not the one with his adoptive parents' names on it)? That would give the name of his mother, and the name of the biological father, if she knew it. It should also give her age and where she was born.
By law, birth records are not available to researchers after 31 Dec 1917, but they can be ordered by descendants of the child. If your father was born in 1954, odds are that his mother was born after 1917 (probably in the 1934-1939) range so her birth record isn't available except to family members either. There was no Florence Harrison born in NSW 1900-1917. Of course, if Harrison were a married name, that wouldn't be in the public domain either.
There were 30 women named Florence Harrison who died in NSW from 1954 through 31 Dec 1986 (the last date that is available to the public). There is no way to tell which one might be her. If she were born in 1934-1939, she would be 77 to 82 years old, if she is still living.
If you have any additional information, please let me know. But there is little in the public domain to help.