William was born at Tumut, New South Wales, in 1851. He is believed to have come from a respective family but on the 24 November 1867, he in the company of John Payne, John Williams and Edward Kelly (no relation to Ned), held up a race meeting at William Whittacker's store, Mossgiel Station, near Willandra. They took a considerable amount from about fifty spectators and while Payne and Kelly left, Brookman and Williams went over to the store. Constable McNamara, who was stationed at Booligal was on the verandah and when the two men bailed him up he made a rush at Brookman. As they struggled Brookman's revolver went off, shattering the constables wrist while another shot hit him in the back of the head. But two men Peerman, the Mossgiel overseer, and a Edward Crombie came to the constable's assistance and helped overpower the two bushrangers.. Placing them in a hut under guard, the police went into pursuit of Kelly and Payne. Payne was soon located and he led the police to Kelly's camp where he lay wounded from an earlier encounter with the law. On 16 January 1868, the four men were tried, whereupon Payne received twenty years gaol, Kelly thirty years, and Brookman and Williams were sentenced to death. The death penalty was later remitted to fifteen years on the road. On 3 July 1874, the Legislative Assembly of New South Wales carried out a lengthy debate on bushrangers, and it was recommended that Brookman be released on 8 July 1874. But his prison record shows that he received remittance of sentence on 8 March 1875, and he was never heard of again.