[After Clink, a district of London famous for its prison.]

and you can still visit it in Southwark, on the South bank, near the Globe theatre, Borough market, and next door to Vinopolis the wine tasting experience. My son has a flat (ok apartment) nr Tower Bridge and we walk past it often enough.

It surprises me that the prison was called after the area, not the other way round. The area is Southwark (Sutherk) and the prison was attached to the Bishop's palace.

Rod