He was the eldest son of John Edward Nassau Molesworth, vicar of Rochdale, Lancashire, and his first wife Harriet; William was born 8 November 1816, at Millbrook, near Southampton, where his father then held a curacy. The engineer Sir Guilford Lindsey Molesworth was his brother. He was educated at the King’s School, Canterbury, and at St. John’s College, Cambridge and Pembroke College, Cambridge, where as a senior optime, he graduated B.A. in 1839. In 1842, he proceeded to the degree of M.A., and in 1883 the university of Glasgow gave him its LL.D. degree.
Molesworth was ordained in 1839, and became curate to his father in Rochdale. In 1841 the warden and fellows of the Manchester Collegiate Church presented him to the incumbency of St. Andrew’s Church, Travis Street, Ancoats, in Manchester, and in 1844 his father presented him to the church of St. Clement, Spotland, near Rochdale. He held that living till his resignation through ill-health in 1889.
An earnest parish priest, in 1881 Molesworth was made an honorary canonry in Manchester Cathedral by Bishop Fraser. He was a high churchman but politically radical. He was the friend of John Bright, who praised one of his histories, and of Richard Cobden, and received information from Lord Brougham for his History of the Reform Bill. He was among the first to support the co-operative movement, which he knew through the Rochdale Pioneers, and served as President of the second day of the 1870 Co-operative Congress, the second to take place.
Though described as ‘angular in manner,’ he appears to have been agreeable and estimable in private life. After some years of ill-health, he died at Rochdale 19 December 1890, and was buried at Spotland.