Francis was the 8^th and youngest child of John and Martha Crossley, founders of the Dean Clough factory.  As well as managing the factory with his two older brothers, he has been credited with the development of the tapestry carpeting, and for his persistence with experiments in the search for a successful power loom. He had the ability to make bold decisions alongside attention to administrative detail.

He was much involved with politics and social issues, was Liberal MP for Halifax and the West Riding for twenty years and made a baronet by Queen Victoria in 1863, mainly in recognition of his charitable activities:  A Congregationalist, he funded the building of Square Church to house a larger congregation than Square Chapel was able to, and worshipped there regularly. He made numerous donations to chapels and schools, established a fund for aged Congregational ministers and their widows, gave the Peoples Park to the town,  founded a group of almshouses in Margaret St, and with his brothers and friend Samuel Porter, founded the Crossley Porter Orphanage, later School. He founded a loan fund to assist both men and women of good character, without security, in setting up in business, and was heard to say : “Whatever pleasure I have had in getting money, I have  had a thousand times more in giving it," 

As well as giving large amounts in private charity to individuals, he was also a supporter of the London Missionary Society.