Brian Colden Antill Pockley was born at North Sydney, New South Wales, on 4 June 1890. Pockley studied medicine at the University of Sydney and was a medical practitioner when the First World War broke out in 1914. At the age of 24, he applied for a commission in the Australian Imperial Force and was appointed as a captain in the Australian Naval and Military Expeditionary Force (ANMEF). He departed Australia to serve with the ANMEF in German New Guinea on 19 August 1914.

Captain Pockley was part of the first landing force of the Naval Brigade at Kabakaul on 11 September 1914. During the advance towards a German wireless station, Able Seaman William Williams was shot in the stomach, becoming the first Australian casualty of the First World War. After tending to Williams, Pockley gave his Red Cross armband to another naval serviceman, Stoker Kember, so Kember could carry Williams to the rear. Shortly afterwards, Pockley was also wounded.

Pockley and Williams were taken aboard HMAS Berrima, where they both died that afternoon. The author of "The Australians at Rabaul", S.S. Mackenzie, later wrote, "Pockley's action in giving up his Red Cross badge, and thus protecting another man's life at the price of his own, was consonant with the best traditions of the Australian army, and afforded a noble foundation for those of Australian Army Medical Corps in the war."

Pockley, with Williams, was buried at Herbertshohe cemetery on 11 September 1914. On 11 July 1919 Brian Pockley's remains were reinterred at Rabaul Cemetery on 11 July 1919, with full naval and military honours. In 1950 his grave was among the First World War graves that were relocated to Rabaul War Cemetery (Bita Paka), Papua New Guinea. Pockley's brother, Lieutenant John Graham Antill Pockley, served with the Australian Army in the First World War and was killed in action, in France, on 30 March 1918.