I think Annitsford lies in the District of North Tyneside.
The community of Annitsford once within the county of Northumberland, was included within the Metropolitan County of Tyne and Wear, on it's formation in 1974.
The county of Tyne and Wear consisted of five Metropolitan Boroughs
( Sunderland, Gateshead and South Tyneside from County Durham, and
Newcastle and North Tyneside, from Northumberland)
When Tyne and Wear County Council was abolished in 1986, it left Annitsford within the Unitary Authority of North Tyneside.
The border between Northumberland and North Tyneside runs north><south between Front Street of Annitsford ( road B1505) and the Spine Road ( Road A189) with Annitsford/North Tyneside on the west, and Northumberland on the east.
Annitsford has enlarged in recent years to the north, and there are several buildings near the junction of Front Street and Road A19. This area is in Northumberland, once the Blyth Valley District.
Adjacent on Front street is a "Welcome to Northumberland" road sign.
Electoral Registers for Annitsford for 1945 will be held at Northumberland County Record Office ( at Woodhorn).
They might be held also at North Shields Library.
I have recently searched Electoral Registers in Blyth Library.
Although I did not specifically seek out those for Annitsford, all I saw for the era in which you are interested, were for Blyth town and it's suburbs, eg Cowpen, Bebside, Newsham.
Michael