Barmston Forge was downstream from High Barmston Farm, on the north bank of the River Wear.

( OED:  Forge - a Blacksmith's Workshop. )

Barmston Forge & Barmston Township - in the Parish of Washington.

( Note the Ferry Landing on the North Bank of the River Wear, just downstream from Orchard Cottage. )

Jean says,
Stephenson's Mill was situated between Middle Barmston Farm and the River Wear, near the Wildfowl Trust entrance.

This watermill was also quite close to Barmston Forge.  It ground corn for, amongst others, Middle & High Barmston Farms.

The Waterwheel that provided power to Barmston Corn Mill.

( Photograph supplied by Jean Potts. )

Washington Wildfowl Trust, Barmston Forge, Stephenson's Mill, Middle & High Barmston Farms.

( This press cutting was supplied by Jean Potts. )