Before his arrival in Australia in 1837, William àBeckett had been active in London literary life, having published several works, including a book of verse (The Siege of Dumbarton Castle and Other Poems). He had also co-edited with his brothers Gilbert (of London Punch fame) and Thomas, the Censor and the Literary Beacon .
àBeckett spent his first nine years in Australia in Sydney, where he was appointed as a judge of the Supreme Court. In 1838, he presented a series of lectures to the Mechanics' School of Arts. These were collected and published in 1839 under the title Lectures on the Poets and Poetry of Great Britain: With an Introductory Lecture on Poetry in General. In 1846, àBeckett became the first resident judge of Port Phillip and in 1852 he was appointed First Chief Justice of Victoria. After a brief, but distinguished career as Chief Justice, ill health forced his retirement in 1857. He returned to England in 1863.
During his time in Australia àBeckett continued his literary activity. He published Lectures on the Poets and Poetry of Great Britain in 1839 and contributed regularly to the Port Phillip Herald under the pseudonym Malwyn. He also edited for a short time Literary News (Sydney). In 1863 he also published a book of verse The Earl's Choice in 1863),