As pointed out in post 6 above, after 1837 Regisitration was based initially on Poor Law Union areas. There were originally four Registration Districts [=R.D.] covering what is
now Birmingham. These were Birmingham [the borough] which was quite tiny at the time!, Aston which covered a much larger area, Kings Norton [which included Smethwick, Harborne, Kings Norton, Northfield & Edgbaston] and last but not least Solihull which included the old parish of Yardley.
In 1912 Yardley R.D. was transferred to Kings Norton R.D.
In 1924 Birmingham R.D. was split into:
Birmingham South R.D. - including Kings Norton R.D. and parts of Birmingham & Aston R.Ds.
Birmingham North R.D. - parts of Birmingham & Aston R.Ds.
In 1932 The above two districts were amlgamated to form Birmingham R.D. but with many sub-districts.
My interest came out of the tangled web of tracing registration on the Wake Green Estate originally in Yardley, then Moseley and now Birmingham
Much interesting information on these changes etc can be seen on
https://www.ukbmd.org.uk/reg/war.html