The Lord Chancellor and the Lord Chief Justice had indicated their intention to remove Dr Andrew Reid from judicial office following the investigation.
But despite being entitled to challenge their decision, the senior coroner decided to stand down.
During her time as deputy assistant coroner, Ms Greenaway conducted 12 inquests in Camden, but worked largely from Poplar Coroner's Court in east London.
According to British law, Ms Greenaway, who also worked as a nurse in Australia, would have needed either five years with the Law Society or five years of experience as a qualified medical practitioner.
She met neither set criteria.
More top news
George Osborne told MPs London would shoulder a large part of his 37% reduction in transport funding.
The prison was originally opened in 1852 as a mixed prison before becoming the first female-only local prison in England in 1902.
A man who tried to help a woman, who was being assaulted by other passengers on the Victoria Line, ended up being punched in the face.