Thanks for the comment, Tal.
I actually got a key when I was still at school, around 17 or 18 years old, and working sometimes till late at night. Before that I was expected to be home in time, before everyone else had gone to bed. I'm not sure whether any of my other friends had one earlier than that. I certainly remember a song that would be sung at someone's 21st birthday party that included two lines that went something like "Now you've got the key to the door, never been twenty-one before" in it. In my early childhood, in England, twenty-one was the age at which a person legally reached adulthood.
Having said that, I do remember that, when I was much younger, my mother would sometimes leave the house key tied to a piece of string hanging inside the letter box of the front door. That way, if she knew she wouldn't be home by the time myself or my siblings got home from school, we could let ourselves in. I think the term latchkey kids is sometimes used to describe such a scenario.