Thank you for your reply, however your Gran's married name was Keddle, where-as the person I am refering to is a single woman named Keddle, and she was, as I mentioned in the original post, born in Chichester. Also as mentioned in the original post, she was staying with a family with the surname of Williamson, in the Stroud area in the 1881 census, and she was, at the time of the census, age 21.
I have since posting that request found out who she is, so I am no longer wondering about her and searching for information about her.