Just to complicate things a little bit more :
The Thomas Moore age 4, is living with mother Hannah age 29, (born Durham, wife of a mariner) and his 2 brothers, William age 6 and Charles age 2, in Byker on 1851 census.
In 1861 census, 4 Smiths Court, Byker, there is a :
Hannah Moore, Head, Widow, age 45, Fruiterer, born Hebron, Durham.
Thomas Moore, son, age 14, born Newcastle,
Charles Moore, son, age 11, born Newcastle,
Alexander Moore, son, age 9, born Newcastle,
Lindre Moore, son, age 6, born Newcastle,
Elizabeth Birril, mother, aged 68, born Barlow, Durham.
In earlier census Elizabeths name is spelt Burrell.
There is a marriage of a Hannah Burrell and a Charles Moore, Newcastle All Saints, Mar 1845.
The John Moore, wife Hannah, in 1841, is a Farmer. There is another John Moore and wife Hannah in 1851 census in Black Callerton, both aged 29, John is a Farm Agent. They have 3 children, but no Thomas.
Alan.