Regarding WHB's address; I have just realized something;
On the Bedford School records of WHB's son Frederick (born in Gwalior) it says that the parents live:-
"Residency, P.O. Gwalior, C. India" Now, I assumed that it meant that their residency could be reached c/o Post Office (box?) in Gwalior

but I have recently found some new information which narrows things down and I think provides more evidence as to this being the WHB (1857-1909) born to William and Sarah, as his place of death was Morar.
"The headquarters of the political officer were situated in the area known as
The Residency, a piece of land measuring 1.17 square miles (3.0 km2) situated close to Morar, about four miles (6 km) to the east of Gwalior fort."