Henry William Challis was educated at Merchant Taylor's School and then in 1859 was admitted to Merton College, Oxford where he studied mathematics.

In 1862 while at Oxford a journal "The Oxford, Cambridge and Dublin Messenger of Mathematics" described as "A journal supported by Junior Mathematical Students and conducted by a Board of Editors" was started and Henry was one of the editors. In that year he contributed a paper entitled "Some Remarks on the Study of Pure Geometry".

He became a Catholic in 1866 and from 1867 taught for a while at the Oratory School in Birmingham where Gerard Manley Hopkins was another teacher.

He left the Catholic Church in 1872 and the following year became a law student at the Inner Temple. In 1876 he was called to the bar. He wrote several books relating to law some of which (including, in 1885, "The Law of Real Property: Chiefly in Relation to Conveyancing") are still on sale today.