Barrett was sentenced to 10 years gaol in 1851 for stealing from trains while working as a switchman for the London & Brighton Railway Company. He arrived in 1851, and his wife Mary and their three children emigrated to join him in 1854. Free in 1858, he became a gardener and the colony’s first commercial nurseryman.
In 1868 he was appointed as Government House Gardener, and by the late 1870s he had been promoted to Head Gardener of the Public Garden and Public Reserves in Perth. Enoch and his second wife Maria also owned a clothing and furniture shop. He died in 1895 aged 83.