Paul Burgess [Brock]'s post with the lyrics to "The Sack Of Southampton" poses the question of Weston / Western Shore.  A locally-significant reference only, but the Western Shore was the beach replaced by Western Esplanade during the '30s land reclamation [which became the Western Docks, inter alia].  This would also fit with the fact that the attack was on the portion of the wall, which indolent merchants had allowed to fall into disrepair, since it meant they didn't have to port their goods [mostly wines, etc.] round via the city gates [which gave directly onto the water, back then], they could lower them down to the ships directly from their premises.
It was this weakness the marauders exploited, and subsequently resulted in fines from the King on those merchants, and an imposition to repair and maintain the walls to prevent repeat incidents.
Humans have always taken the 'easy' way out!