Sexton was born in Newcastle upon Tyne on 13 April 1856 to an Irish-born family of market traders, who soon moved to St Helens, Lancashire. After leaving school he worked in a variety of jobs, including as a seaman and in a chemical factory, before becoming a docker on Liverpool Docks. In 1884 he set up his own business as a coal merchant.
Sexton's life story is characterized by a journey from childhood to adulthood, marked by diverse work experiences and entrepreneurial endeavors. He began with humble beginnings as a child of Irish-born market traders before transitioning into various jobs like seaman and chemical factory worker. His career culminated in establishing his own coal merchant business in 1884.