From what I can work out, the name of Vauxhall Bridge may be derived from the Vauxhall Pleasure Gardens that were, for a while, somewhere in the Dowry Square vicinity, themselves named for the famous London original (as mentioned in Fanny Burney's Evelina, among other books) Not sure what the through line is, though, as the pleasure gardens in Bristol weren't that long-lived, and of course the New Cut is significantly newer, so it's not like there would have been a bridge here back then.
GPS Coordinates:
51.44605, -2.61048
Location: Coronation Road West