There are only 47 Ullathorne's showing in the index for the 1871 census, but none of them are shown as being born Reading or even Berkshire. Its possible that they are there under a different spelling, so I'll check some others.
If you have any other information about Emily that would help, let me know.
hi terry my name is christine and I thought you might like to know that my grt grandmother was Adelaide Ullathorne daughter of Emma Hill and John Ullathorne and younger sister to Emily.