Great Bridge would come under one of the Tipton parishes:
St John (Registers 1854-1978)
St Martin (Registers 1573-1901)
St Paul (Registers from 1839)
GenUKI says, re Tipton:
Tipton Green, the largest village in Tipton parish, is one and a half miles N of Dudley, and three miles S of Bilston, and consists of a number of populous streets, with several wharfs, manufactories, and retail shops. Branching eastward are the neighbouring villages of Bloomfield, Burnt-Tree, Dudley Port, and Horseley Heath, the three latter of which form one continuous street of houses and manufactories, extending two miles on the Birmingham road, and a little beyond them are the large villages of Toll-End and Great Bridge, the latter of which is partly in West Bromwich.
And GenUKI also says, of West Bromwich:
The other principal assemblages of houses and streets are Swan Village, Hill-Top, Spon Lane, and Great Bridge, the latter of which is partly in Tipton parish.
So, maybe you also need to look at West Bromwich?