By 1322 there is scant record of a fulling mill, showing the early beginnings of textile manufacture in Manchester. This mill was located somewhere alongside the Cathedral, and the alleyway known as "Hanging Ditch" still marks the course of the River Irk where it enters the Irwell, where textiles were hung to drain and drip dry after fulling. The Grelley manor, (now Chetham's School of Music), was fortified on three sides as it overlooked the River Irk on one side, a tributary ditch on another side and the River Irwell on another - it was therefore a superb defensive position, standing high on a sandstone bluff with effective natural defences.
Subsequently, the River Irk was culvetted below ground under what is now Walkers Croft and Hanging Ditch. Beside the cathedral one can still see the remains of "Hanging Bridge" where the medieval bridge crossed Hanging Ditch. A wooden bridge crossed the Irwell in front of the Manor, and was replaced by a stone three-arch bridge in the 14th century, on the site of where Victoria Bridge (built in 1839) now stands.
Manchester became a Baronial Borough (thereby an independent self-governing entity) in 1301, still ruled by the Lord of the Manor, but with an appointed "boroughreeve" (or Mayor) who handled day-to-day administration of the borough. Manchester was to change very little thereafter until the 16th century.
I think you're right Tony, it's not to do with hangings - just a bridge that overhang the river which is underground (dried up?)