The Freedom, which allows its recipients to walk sheep over London Bridge, is typically awarded to individuals nominated by corporation councillors.
Mountbatten-Windsor inherited the status as the child of a Freeman and constitutes a legal right.
The corporation said: “Applications via patrimony are not considered by our elected members.
“We have carefully considered whether it is possible to remove a Freedom granted by patrimony and understand that we are not able to do so.”
Though today largely a ceremonial honour the Freedom is still awarded to individuals on a regular basis.
Sir Lenny Henry and Cate Blanchett are among those to have received the honour.