In medieval London the Bishop of Winchester (e.g. William of Wykeham) had a Palace on the section of the south bank of the Thames nearest here. It included what is now Southwark Cathedral and the building which is now a romantic ruin in Clink Street.
At the time many of the disreputable pleasures that men engaged in, such as theatre, bear-baiting and prostitutes were banned from the City of London which meant they flourished across the river, here in the area under the Bishop's jurisdiction, his manor. His response to the presence of the brothels was to treat them as any other business so he licensed and taxed them, hence "Winchester Geese".