Brookman was born 15 April 1850 in Glasgow, Scotland, the eldest son of typesetter Benjamin Brookman (16 September 1826 - 11 June 1917) and his wife Jane née Wilson (d. 1 March 1881) [REF].
He stood successfully for the Central District vacancy in South Australia's Legislative Council in 1901[REF] caused by the resignation of Charles Kingston, who took up a seat in the new Federal Parliament.