In 1829, Brockman, with his wife and eldest son Edmund, emigrated to the Swan River Colony in Western Australia.

His success as a farmer prompted his wife's brother Edward Hamersley to immigrate.

He called the property Cheriton after the parish of his father, the Reverend Julius Drake-Brockman.

Due to favourable soils, the property became the principal source of citrus fruit for Perth, and was especially known for what came to be called Cheriton oranges.

He contested the seat of Swan in the subsequent election, but was defeated by Thomas Courthope Gull.

Two of his sons, Henry and Edmund Ralph, became farmers in the colony and Members of the Legislative Council.