He obtained a doctorate from the University of Manchester in 1951, on the 19th century history of St Helens.
This led to his first book, co-written with a school contemporary, John Harris, who had been researching St Helens in the 18th century.
A Merseyside Town in the Industrial Revolution (1954) was influential in the emerging field of urban history.
After teaching at the University of Aberdeen for 1 year, Barker taught at the London School of Economics between 1953 and 1964, when he became Professor of Economic and Social History at the newly established University of Kent.
He served as president of the Railway and Canal Historical Society, as founding chairman of the Oral History Society and as secretary and then chairman of the British National Committee of Historians.