Why is The Mall pronounced differently even though it shares the same spelling as mall (shopping)?
The street in London actually comes from the French "pêle-mêle" meaning:
From various online dictionaries:
The French pronunciation is likely where the "a as in gal" sound comes from.
When the portmanteau pall-mall/pell-mell sprouted up, according to Etymonline mall began meaning "shaded walk serving as a promenade". These walkways/alleys had become common places to play a game similar to croquet by the name of pall-mall. The street in question was originally such an alley.
At the same time usage began to drift from the French sounding "a as in gal" to a, perhaps more British, "a as in ball". When we finally got to the point where mall gained it's current meaning, the common usage was the latter but as the street is a proper name predating this change, so I assume it has simply kept the sounds originally ascribed to it.