Could be a Smiths Dock tug. It is taking a barge possibly for the Tees Dredger. When the barge was full of silt from the river bed, a tug would take it out to sea, dump the silt and bring the barge back to the Dredger. (This information was kindly provided by Gordon Crawford)
Could this be the ferry which carried passengers across the Tees – situated near Victoria bridge? (This information was kindly provided by Sarah Sheraton) 
Picture Stockton Archive
A Pictorial History of Stockton-on-Tees
The Tug in this picture is the “Francis Samuelson” belonging to the Tees Conservancy Commissioners. She was built by Smith”s Dock”s just before W.W.2 and her engineroom was based on the Smiths Dock built Whaler”s, she had one boiler which was coal-fired.
The tug is the Francis Samuelson belonging to the Tees Conservancy Commissioners carrying an empty barge, passing Acklam Steel Works with Haverton Hill Shipyard in the background.