Sally - have you got the birth certificate for Elizabeth who was 9 in 1881 ?
The problem I hit was this:
The Elizabeth who was 4 in the 1861 census, and who I thought must have died since they subsequently had another daughter Elizabeth, as still there in 1871 :
1871
RG10. P. 5056 Fol. 53 Pg. 9Church Street, Gateshead
Mary Leve Head Wid 38 Hawker
Margaret Dau 23
Mary Dau 20 Pipe trimmer
Elizabeth Dau 13 Factory Girl (tobacco)
all born Gateshead.
So Mary was already a Widow in 1871; death reg for Joseph :
age 47 Gateshead Q4.
1867 Vol. 10a. Pg. 409
This is why I ask if you have the birth certificate for Elizabeth b. 1871

It does not seem that she was the daughter of Joseph and Mary, as you say in your first post

Elizabeth born 1858 went on to marry John Greenup in 1878, and in 1891 Mary is living with them: do you want that record ?
There are two Levi grandchildren living there also, Ellen age 7 and James age 2, together with daughter Margaret.