It's very hard to tell using google maps, but in my book I'm writing that All-Hallows by the Tower is in the Whitechapel area/borough of London (in the 1930s). I'd hate to get this wrong but I can find a map with the boundaries clearly delineated.
All Hallows is within the City of London. The Tower itself is in Tower Hamlets Borough, and in the '30s was actually in the former borough of Stepney. Whitechapel proper is a bit to the North and East of the Tower, though speaking loosely you could say the tower is within it. A map from Wikipedia shows the outlines of the former parishes- All Hallows' parish is the first white area to the West of the Tower.
OpenStreetMap shows the boundaries- All Hallows church is definitely within the City all bar, it seems, a sliver of the extension you can see in Google's satellite view.
