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1778 Born. His father was Richard Birley (1743–1812), merchant, who had four sons and four daughters. One of Hugh's brother was Joseph Birley (1782–1847)
1814 Began building Cambridge Street Mill, Chorlton-on-Medlock.
Birley was a local magistrate and one of the commanders of the Manchester & Salford Yeomanry responsible for the Massacre at St Peter's Field in 1819.
1822 Hugh Hornby Birley, in Manchester, married Cecily Hornby (1797-1843), of Kirkham. Their children included William Hornby Birley (1834-1921), Edward Hornby Birley (1834-8), Joseph Hornby Birley (1827-1881), Rev Edward Hornby Birley (1842-1928). 
1837 Met John George Bodmer and offered to help him commercialise his inventions, transferring his tools, patterns, and machines to Manchester, where he made a room available at the Chorlton Mills, belonging to Messrs. Birley and Co.
1839 He was also instrumental in founding the Royal Victoria Gallery of Practical Science
At a later date, Mr Birley purchased a nearby foundry, which was adapted to Bodmer's needs.
He was associated with the Royal Manchester Institution and with the establishment of Owens College, Manchester. He was a director of the Manchester Gas Works and became a business associate of Charles Macintosh with the intention of putting the works' waste products to profitable use in the manufacture of waterproof fabrics.
1845 Died in Eccles. Hugh Hornby Birley was buried in the family vault in St. Peter's Church, Manchester.