"Winchester Geese" was a slang name for the prostitutes who worked in the areas of Southwark and Bankside. They were licensed by the Bishop of Winchester, whose elegant palace sat nearby, and to whom they paid taxes and licence fees.
The remains of the Palace can still be seen on Clink Street in Southwark, although only a rose window and foundations remain today. You can also still see the notorious Cross Bones cemetery in Southwark. Although it is now paved over, a makeshift shrine has been created at the gates to honour the prostitutes and paupers who were buried here unmarked in unconsecrated ground, as the Bishop wouldn't allow his geese to be buried in the correct, and holy, manner.
Winchester Goose was also a slang term for venereal disease during the 17th and 18th centuries.