"Ne less than a tunnel thro' under the 'Tyne":- Ralph Dodd, a civil engineer (died 1822) proposed a tunnel under the Tyne between North and South Shields. He also proposed the Thames Tunnel later built by Brunel. [Ref: Daily News 4th May 1925 "An Old Shields Tunnel Project"]
The ferry run by the North and South Shields Ferry Company began service in 1829. However; steamers had been carrying passengers on the Tyne since 1818 [Ref: Lewenhak, Sheila. Steamships and Shipbuilders of the Industrial Revolution]. The use of the future tense (e.g. "Then away to St Steven's, and get a Steam Act" and "But we ne'er need delay, if we a had Steam Ferry") suggests that the song predates the establishment of the ferry.