Just a bit of georgraphic background....to help or maybe hinder !
Although generally speaking the River Tyne was the main north/south border between the traditional counties of Northumberland (NMB) and Durham, a blob of NMB lay/lies on the southern side of the Tyne, which includes Mickley,Prudhoe, etc.
The Stanley Burn defined the east/west border between NMB and Co Durham. Mickley is about 2-3 miles away on the west (NMB) side. On the east (Co Durham)side of the Burn are places such as Crawcrook, Greenside, Chopwell etc.
Mickley, as Linda has already pointed out, lay within the wide Hexham Registration District. Crawcrook etc lay within the Gateshead Registration District.
So a birth in Mickley would have to have been registered With Hexham Reg Dist, but a birth just a couple of miles east of Mickley would have to have been registered with the Gateshead Reg District..... ??
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Parents were allowed 42 days grace in which to register their child. If they moved home, maybe into another Reg Dist, before they had registered their child, they would have had to register in the correct (i.e. birth) Reg District.
( I have an instance in my tree where the parents of a Blyth-born child moved to Sunderland before registering the child with Tynemouth Reg Dist. They then "registered" at Sunderland, the "wrong" Reg Dist. But Sunderland informed Tynemouth, who put the records straight ! )
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Maybe a garden-path direction, but the birth of a Robert William was registered in Jan Qtr 1903, with Hexham reg Dist, but surname was Ferguson ?
Michael Dixon