Harrison was born in Fulham, Middlesex, moving to Sunderland at a young age. He first worked on the railways as Assistant to T L Gooch (1808-1882) surveying part of the London and Birmingham Railway for Robert Stephenson (1803-1859). He became the engineer for the Stanhope and Tyne Railway in 1832 and of the Durham Junction Railway in 1834. He worked as resident engineer under Robert Stephenson in the construction of the Newcastle and Darlington Junction and Newcastle and Berwick Railways, completing the east coast rail route in England. Harrison became the chief engineer and general manager of the York, Newcastle and Berwick Railway in 1849 and in 1854 he became chief engineer of the North Eastern Railway with the amalgamation of the York, Newcastle and Berwick, York and North Midland, and Leeds Northern Companies. He was elected president of the Institution of Civil Engineers in 1873.