Learn English – Seen pronounced ‘sin’

The street in London actually comes from the French "pêle-mêle" meaning:

From various online dictionaries:

1. any old how, at random, chaotically
2. In a jumbled, confused manner; helter-skelter.
3. In frantic disorderly haste; headlong

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.

My parents are both from Northern Britain, my mother from Newcastle upon Tyne and my father from Glasgow. They both say "Wed'nzday". By contrast, I was brought up and live in the South-west of England, where the local pronunciation is "Wenzday"