Perusing the 1894 ordnance map of Berner Street a couple of observations.
When Schwartz turned into Berner Street and saw 'some distance in front of him' BS man, it could be that BS man had walked from Back Church Lane onto Berner Street through Sander Street.
Also on the map it does appear that climbing over a couple of roof tops from Dutfield yard would allow an exit for the murderer onto Back Church Lane.
Just observations
NW
When Schwartz turned into Berner Street and saw 'some distance in front of him' BS man, it could be that BS man had walked from Back Church Lane onto Berner Street through Sander Street.
Also on the map it does appear that climbing over a couple of roof tops from Dutfield yard would allow an exit for the murderer onto Back Church Lane.
Just observations
NW

It does seem a bit extreme though, don't you think?
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