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Herbert was born on March 14th 1853 as the oldest son of Sir Thomas Storey and his first wife, Eliza Anne Sherren, who passed away when Herbert was eight years old. His father was also a prominent philanthropist in Lancaster, as well as an important local political figure, as Herbert grew up to be. His father was on Lancaster's Town Council between 1862 and 1890, while also being elected mayor in 1867, 1873, 1874, and again in 1887. Thomas also founded Storey Bros and Co. with his brothers, Edward and William, and also Edmund Sharpe. The company, like Williamson's, produced oilcloth and leathercloth. In 1887, the last year that Thomas was Mayor, and also the year of the Queen's Jubilee, he opened the Storey Institute in Lancaster, a place for technical and art education.
In the 1860s, Herbert attended Lancaster Royal Grammar School before later attending the Grammar School at Derby. Afterwards, he went to London to train with W. and R. Morley, before returning to Lancaster to train at a mechanics' shop at Moor Lane mill. Herbert then went to engineering works in Salford for a year, before studying Chemistry at the University of Manchester for two years, and later spent half a year at Leipzig to study.
Herbert began a successful career in business, and like his father, became a prominent local political figure, and a renowned philanthropist in Lancaster.