Cannot give you an "A" for north-east Geography LOL.
Hebburn on Tyne ( on the south bank of the river) was in the "traditional" County Durham, never in Northumberland.
In 1970 bureaucrats decided to take the south-eastern part of Northumberland and the north-eastern part of County Durham, merge them, to form the new county of Tyne & Wear. (Similar changes happened throughout England Scotland and Wales)
Then in 1986 Tyne and Wear as a "normal" county was disbanded leaving what we have today.. i.e. Five separate
" Unitary Authorities" of North Tyneside, Newcastle, on the north side of River Tyne, and South Tynseide, Gateshead and Sunderland , south of the Tyne.
For some functions the separate units work independently of each other, for others they work jointly.
Hebburn today lies within the unitary authority of South Tyneside.
(which is neither Northumberland or County Durham)
"Ancient" Parishes were the forerunners of local authorities. Before 1875, Hebburn on Tyne lay within the parish of Jarrow. In 1875 Hebburn became an independent parish.
Michael Dixon
Newcastle