Barnett was a prominent portrait photographer of the late 19th and early 20th centuries, establishing the successful Falk studios in Sydney.

[2] He was known in particular for photographing stage stars and other celebrities; one of his best-known sitters was Sarah Bernhardt, who sat for him while visiting Australia in 1891.

He exhibited a collection of photographs of British Armed Forces personnel of World War I in 1917, titled Warriors All.

[6] Barnett sold his London studios in 1920 and moved to Dieppe, France, where he maintained a keen interest in contemporary French art.

[2] In 1896 Barnett met French cinematographer Marius Sestier, an agent of early filmmakers the Lumière brothers assigned to demonstrate their cinématographe abroad.