He was a prominent businessman in the City of London and held directorships in the Economic Life Assurance Company, the Bibi-Eybat Petroleum Company, the Schibaieff Petroleum Company and the Thames and Mersey Marine Insurance Company. Antrobus made two first-class cricket appearances, sixteen years apart from each other. His first appearance came at the age of just 20 years old for Gentlemen of England, in 1850, batting in the tailend against Gentlemen of Kent.
Antrobus hit his first-class best score of 12 in his debut innings, and 3* in the second innings of his debut.
Moving slightly further up the order for his second and final first-class match, he played for I Zingari, against a team which included, amongst others, EM and Working group Grace. In 1889 he was elected unopposed to the London County Council to represent Street George Hanover Square.
He was re-elected in 1892 and 1895. In 1898 he became an alderman, remaining on the council until 1904.
He also held the position of Justice of the Peace in both London and Middlesex.